a solid cylinder rolls without slipping down an incline

At steeper angles, long cylinders follow a straight. How do we prove that Any rolling object carries rotational kinetic energy, as well as translational kinetic energy and potential energy if the system requires. From Figure $\PageIndex{2}$(a), we see the force vectors involved in preventing the wheel from slipping. Thus, [latex]\omega \ne \frac{{v}_{\text{CM}}}{R},\alpha \ne \frac{{a}_{\text{CM}}}{R}[/latex]. It reaches the bottom of the incline after 1.50 s then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, The sum of the forces in the y-direction is zero, so the friction force is now fk=kN=kmgcos.fk=kN=kmgcos. (b) What condition must the coefficient of static friction $\mu_{S}$ satisfy so the cylinder does not slip? of mass is moving downward, so we have to add 1/2, I omega, squared and it still seems like we can't solve, 'cause look, we don't know This thing started off We see from Figure 11.4 that the length of the outer surface that maps onto the ground is the arc length RR. This distance here is not necessarily equal to the arc length, but the center of mass In rolling motion with slipping, a kinetic friction force arises between the rolling object and the surface. How fast is this center [/latex], [latex]{a}_{\text{CM}}=\frac{mg\,\text{sin}\,\theta }{m+({I}_{\text{CM}}\text{/}{r}^{2})}. If the driver depresses the accelerator slowly, causing the car to move forward, then the tires roll without slipping. Now let's say, I give that If the cylinder falls as the string unwinds without slipping, what is the acceleration of the cylinder? conservation of energy says that that had to turn into A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). Mechanical energy at the bottom equals mechanical energy at the top; [latex]\frac{1}{2}m{v}_{0}^{2}+\frac{1}{2}(\frac{1}{2}m{r}^{2}){(\frac{{v}_{0}}{r})}^{2}=mgh\Rightarrow h=\frac{1}{g}(\frac{1}{2}+\frac{1}{4}){v}_{0}^{2}[/latex]. So, how do we prove that? driving down the freeway, at a high speed, no matter how fast you're driving, the bottom of your tire [/latex] The coefficients of static and kinetic friction are [latex]{\mu }_{\text{S}}=0.40\,\text{and}\,{\mu }_{\text{k}}=0.30.[/latex]. Including the gravitational potential energy, the total mechanical energy of an object rolling is, \[E_{T} = \frac{1}{2} mv^{2}_{CM} + \frac{1}{2} I_{CM} \omega^{2} + mgh \ldotp\]. So no matter what the what do we do with that? These equations can be used to solve for [latex]{a}_{\text{CM}},\alpha ,\,\text{and}\,{f}_{\text{S}}[/latex] in terms of the moment of inertia, where we have dropped the x-subscript. whole class of problems. Examples where energy is not conserved are a rolling object that is slipping, production of heat as a result of kinetic friction, and a rolling object encountering air resistance. Consider a solid cylinder of mass M and radius R rolling down a plane inclined at an angle to the horizontal. An object rolling down a slope (rather than sliding) is turning its potential energy into two forms of kinetic energy viz. speed of the center of mass, I'm gonna get, if I multiply What is the moment of inertia of the solid cyynder about the center of mass? A hollow cylinder is on an incline at an angle of 60. So that's what we're A solid cylinder of mass `M` and radius `R` rolls down an inclined plane of height `h` without slipping. Direct link to Anjali Adap's post I really don't understand, Posted 6 years ago. Both have the same mass and radius. When travelling up or down a slope, make sure the tyres are oriented in the slope direction. Use Newtons second law of rotation to solve for the angular acceleration. either V or for omega. Why is there conservation of energy? of mass of the object. Since the wheel is rolling, the velocity of P with respect to the surface is its velocity with respect to the center of mass plus the velocity of the center of mass with respect to the surface: Since the velocity of P relative to the surface is zero, vP=0vP=0, this says that. At the top of the hill, the wheel is at rest and has only potential energy. baseball rotates that far, it's gonna have moved forward exactly that much arc The ramp is 0.25 m high. consent of Rice University. Smooth-gliding 1.5" diameter casters make it easy to roll over hard floors, carpets, and rugs. Suppose a ball is rolling without slipping on a surface( with friction) at a constant linear velocity. We have, Finally, the linear acceleration is related to the angular acceleration by. These equations can be used to solve for aCM, $\alpha$, and fS in terms of the moment of inertia, where we have dropped the x-subscript. Cylinders Rolling Down HillsSolution Shown below are six cylinders of different materials that ar e rolled down the same hill. To analyze rolling without slipping, we first derive the linear variables of velocity and acceleration of the center of mass of the wheel in terms of the angular variables that describe the wheels motion. Remember we got a formula for that. At least that's what this If we substitute in for our I, our moment of inertia, and I'm gonna scoot this It is worthwhile to repeat the equation derived in this example for the acceleration of an object rolling without slipping: \[a_{CM} = \frac{mg \sin \theta}{m + \left(\dfrac{I_{CM}}{r^{2}}\right)} \ldotp \label{11.4}\]. We then solve for the velocity. V and we don't know omega, but this is the key. Since the wheel is rolling, the velocity of P with respect to the surface is its velocity with respect to the center of mass plus the velocity of the center of mass with respect to the surface: Since the velocity of P relative to the surface is zero, [latex]{v}_{P}=0[/latex], this says that. If we differentiate Equation \ref{11.1} on the left side of the equation, we obtain an expression for the linear acceleration of the center of mass. "Rollin, Posted 4 years ago. Sorted by: 1. In order to get the linear acceleration of the object's center of mass, aCM , down the incline, we analyze this as follows: Two locking casters ensure the desk stays put when you need it. Substituting in from the free-body diagram. on its side at the top of a 3.00-m-long incline that is at 25 to the horizontal and is then released to roll straight down. 8 Potential Energy and Conservation of Energy, [latex]{\mathbf{\overset{\to }{v}}}_{P}=\text{}R\omega \mathbf{\hat{i}}+{v}_{\text{CM}}\mathbf{\hat{i}}. another idea in here, and that idea is gonna be At low inclined plane angles, the cylinder rolls without slipping across the incline, in a direction perpendicular to its long axis. baseball's distance traveled was just equal to the amount of arc length this baseball rotated through. Project Gutenberg Australia For the Term of His Natural Life by Marcus Clarke DEDICATION TO SIR CHARLES GAVAN DUFFY My Dear Sir Charles, I take leave to dedicate this work to you, [/latex] The value of 0.6 for [latex]{\mu }_{\text{S}}[/latex] satisfies this condition, so the solid cylinder will not slip. [latex]\frac{1}{2}{v}_{0}^{2}-\frac{1}{2}\frac{2}{3}{v}_{0}^{2}=g({h}_{\text{Cyl}}-{h}_{\text{Sph}})[/latex]. So recapping, even though the There's gonna be no sliding motion at this bottom surface here, which means, at any given moment, this is a little weird to think about, at any given moment, this baseball rolling across the ground, has zero velocity at the very bottom. [/latex], Newtons second law in the x-direction becomes, The friction force provides the only torque about the axis through the center of mass, so Newtons second law of rotation becomes, Solving for [latex]\alpha[/latex], we have. Newtons second law in the x-direction becomes, \[mg \sin \theta - \mu_{k} mg \cos \theta = m(a_{CM})_{x}, \nonumber\], \[(a_{CM})_{x} = g(\sin \theta - \mu_{k} \cos \theta) \ldotp \nonumber\], The friction force provides the only torque about the axis through the center of mass, so Newtons second law of rotation becomes, \[\sum \tau_{CM} = I_{CM} \alpha, \nonumber\], \[f_{k} r = I_{CM} \alpha = \frac{1}{2} mr^{2} \alpha \ldotp \nonumber\], \[\alpha = \frac{2f_{k}}{mr} = \frac{2 \mu_{k} g \cos \theta}{r} \ldotp \nonumber\]. [/latex], [latex]{v}_{\text{CM}}=\sqrt{(3.71\,\text{m}\text{/}{\text{s}}^{2})25.0\,\text{m}}=9.63\,\text{m}\text{/}\text{s}\text{. travels an arc length forward? about that center of mass. [/latex] The coefficient of static friction on the surface is [latex]{\mu }_{S}=0.6[/latex]. $(b)$ How long will it be on the incline before it arrives back at the bottom? Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. There is barely enough friction to keep the cylinder rolling without slipping. If we look at the moments of inertia in Figure 10.20, we see that the hollow cylinder has the largest moment of inertia for a given radius and mass. By the end of this section, you will be able to: Rolling motion is that common combination of rotational and translational motion that we see everywhere, every day. the point that doesn't move, and then, it gets rotated Well imagine this, imagine the radius of the cylinder times the angular speed of the cylinder, since the center of mass of this cylinder is gonna be moving down a So Normal (N) = Mg cos 1 Answers 1 views Understanding the forces and torques involved in rolling motion is a crucial factor in many different types of situations. (b) What is its angular acceleration about an axis through the center of mass? Point P in contact with the surface is at rest with respect to the surface. unwind this purple shape, or if you look at the path A solid cylinder and a hollow cylinder of the same mass and radius, both initially at rest, roll down the same inclined plane without slipping. From Figure $\PageIndex{7}$, we see that a hollow cylinder is a good approximation for the wheel, so we can use this moment of inertia to simplify the calculation. Use Newtons second law of rotation to solve for the angular acceleration. Note that the acceleration is less than that for an object sliding down a frictionless plane with no rotation. Answer: aCM = (2/3)*g*Sin Explanation: Consider a uniform solid disk having mass M, radius R and rotational inertia I about its center of mass, rolling without slipping down an inclined plane. A solid cylinder rolls down an inclined plane without slipping, starting from rest. The acceleration will also be different for two rotating cylinders with different rotational inertias. (b) If the ramp is 1 m high does it make it to the top? Direct link to JPhilip's post The point at the very bot, Posted 7 years ago. What is the angular acceleration of the solid cylinder? In the absence of any nonconservative forces that would take energy out of the system in the form of heat, the total energy of a rolling object without slipping is conserved and is constant throughout the motion. Thus, the hollow sphere, with the smaller moment of inertia, rolls up to a lower height of [latex]1.0-0.43=0.57\,\text{m}\text{.}[/latex]. [/latex], [latex]{f}_{\text{S}}={I}_{\text{CM}}\frac{\alpha }{r}={I}_{\text{CM}}\frac{({a}_{\text{CM}})}{{r}^{2}}=\frac{{I}_{\text{CM}}}{{r}^{2}}(\frac{mg\,\text{sin}\,\theta }{m+({I}_{\text{CM}}\text{/}{r}^{2})})=\frac{mg{I}_{\text{CM}}\,\text{sin}\,\theta }{m{r}^{2}+{I}_{\text{CM}}}. Thus, the velocity of the wheels center of mass is its radius times the angular velocity about its axis. Since the wheel is rolling without slipping, we use the relation [latex]{v}_{\text{CM}}=r\omega[/latex] to relate the translational variables to the rotational variables in the energy conservation equation. that these two velocities, this center mass velocity Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . Only available at this branch. This is the speed of the center of mass. up the incline while ascending as well as descending. Which of the following statements about their motion must be true? [latex]\frac{1}{2}m{v}_{0}^{2}+\frac{1}{2}{I}_{\text{Sph}}{\omega }_{0}^{2}=mg{h}_{\text{Sph}}[/latex]. respect to the ground, which means it's stuck The situation is shown in Figure. From Figure, we see that a hollow cylinder is a good approximation for the wheel, so we can use this moment of inertia to simplify the calculation. It has mass m and radius r. (a) What is its acceleration? The answer is that the. The free-body diagram is similar to the no-slipping case except for the friction force, which is kinetic instead of static. We see from Figure $\PageIndex{3}$ that the length of the outer surface that maps onto the ground is the arc length R$\theta$. For no slipping to occur, the coefficient of static friction must be greater than or equal to $\frac{1}{3}$tan $\theta$. Archimedean solid A convex semi-regular polyhedron; a solid made from regular polygonal sides of two or more types that meet in a uniform pattern around each corner. You should find that a solid object will always roll down the ramp faster than a hollow object of the same shape (sphere or cylinder)regardless of their exact mass or diameter . Fingertip controls for audio system. How much work does the frictional force between the hill and the cylinder do on the cylinder as it is rolling? (b) What condition must the coefficient of static friction \ (\mu_ {S}\) satisfy so the cylinder does not slip? the center of mass of 7.23 meters per second. As the wheel rolls from point A to point B, its outer surface maps onto the ground by exactly the distance travelled, which is [latex]{d}_{\text{CM}}. It has mass m and radius r. (a) What is its acceleration? In the case of slipping, [latex]{v}_{\text{CM}}-R\omega \ne 0[/latex], because point P on the wheel is not at rest on the surface, and [latex]{v}_{P}\ne 0[/latex]. The moment of inertia of a cylinder turns out to be 1/2 m, ground with the same speed, which is kinda weird. (b) Will a solid cylinder roll without slipping Show Answer It is worthwhile to repeat the equation derived in this example for the acceleration of an object rolling without slipping: aCM = mgsin m + ( ICM/r2). Can a round object released from rest at the top of a frictionless incline undergo rolling motion? This is done below for the linear acceleration. Since the wheel is rolling, the velocity of P with respect to the surface is its velocity with respect to the center of mass plus the velocity of the center of mass with respect to the surface: \[\vec{v}_{P} = -R \omega \hat{i} + v_{CM} \hat{i} \ldotp\], Since the velocity of P relative to the surface is zero, vP = 0, this says that, \[v_{CM} = R \omega \ldotp \label{11.1}\]. The information in this video was correct at the time of filming. For no slipping to occur, the coefficient of static friction must be greater than or equal to [latex](1\text{/}3)\text{tan}\,\theta[/latex]. In other words, the amount of Solid Cylinder c. Hollow Sphere d. Solid Sphere step by step explanations answered by teachers StudySmarter Original! A hollow sphere and a hollow cylinder of the same radius and mass roll up an incline without slipping and have the same initial center of mass velocity. speed of the center of mass, for something that's We then solve for the velocity. A cylinder is rolling without slipping down a plane, which is inclined by an angle theta relative to the horizontal. right here on the baseball has zero velocity. The only nonzero torque is provided by the friction force. the tire can push itself around that point, and then a new point becomes Bought a $1200 2002 Honda Civic back in 2018. We have, \[mgh = \frac{1}{2} mv_{CM}^{2} + \frac{1}{2} mr^{2} \frac{v_{CM}^{2}}{r^{2}} \nonumber\], \[gh = \frac{1}{2} v_{CM}^{2} + \frac{1}{2} v_{CM}^{2} \Rightarrow v_{CM} = \sqrt{gh} \ldotp \nonumber\], On Mars, the acceleration of gravity is 3.71 m/s2, which gives the magnitude of the velocity at the bottom of the basin as, \[v_{CM} = \sqrt{(3.71\; m/s^{2})(25.0\; m)} = 9.63\; m/s \ldotp \nonumber\]. slipping across the ground. Also, in this example, the kinetic energy, or energy of motion, is equally shared between linear and rotational motion. Since there is no slipping, the magnitude of the friction force is less than or equal to $\mu_{S}$N. Writing down Newtons laws in the x- and y-directions, we have. Relevant Equations: First we let the static friction coefficient of a solid cylinder (rigid) be (large) and the cylinder roll down the incline (rigid) without slipping as shown below, where f is the friction force: On the right side of the equation, R is a constant and since =ddt,=ddt, we have, Furthermore, we can find the distance the wheel travels in terms of angular variables by referring to Figure 11.4. The coefficient of static friction on the surface is s=0.6s=0.6. Show Answer It is surprising to most people that, in fact, the bottom of the wheel is at rest with respect to the ground, indicating there must be static friction between the tires and the road surface. When an object rolls down an inclined plane, its kinetic energy will be. It's a perfect mobile desk for living rooms and bedrooms with an off-center cylinder and low-profile base. Point P in contact with the surface is at rest with respect to the surface. Starts off at a height of four meters. All Rights Reserved. Video walkaround Renault Clio 1.2 16V Dynamique Nav 5dr. David explains how to solve problems where an object rolls without slipping. Got a CEL, a little oil leak, only the driver window rolls down, a bushing on the front passenger side is rattling, and the electric lock doesn't work on the driver door, so I have to use the key when I leave the car. When an ob, Posted 4 years ago. Legal. A cylindrical can of radius R is rolling across a horizontal surface without slipping. This is why you needed Therefore, its infinitesimal displacement d$\vec{r}$ with respect to the surface is zero, and the incremental work done by the static friction force is zero. The sum of the forces in the y-direction is zero, so the friction force is now [latex]{f}_{\text{k}}={\mu }_{\text{k}}N={\mu }_{\text{k}}mg\text{cos}\,\theta . and this angular velocity are also proportional. translational kinetic energy, 'cause the center of mass of this cylinder is going to be moving. What if we were asked to calculate the tension in the rope (problem, According to my knowledge the tension can be calculated simply considering the vertical forces, the weight and the tension, and using the 'F=ma' equation. About its axis are oriented in the slope direction Newtons second law of rotation to solve the... Cylinder rolls down an inclined plane without slipping down a plane, its kinetic energy, 'cause the of... Ascending as well as descending cylinder as it is rolling without slipping down plane. Tyres are oriented in the slope direction than that for an object rolling down a plane inclined at angle. Cylinder and low-profile base be true understand, Posted 6 years ago different rotational.... Content produced by OpenStax is licensed under a Creative Commons Attribution License to JPhilip 's post point... Statements about their motion must be true 1/2 m, ground with the surface and we n't. We do with that steeper angles, long cylinders follow a straight coefficient static... Be different for two rotating cylinders with different rotational inertias oriented in the slope direction how much does! Roll over hard floors, carpets, and rugs are oriented in the slope direction mass of this is. Without slipping times the angular acceleration by only potential energy into two forms of kinetic energy viz angles, cylinders. Is kinda weird the amount of arc length this baseball rotated through v and we do n't understand Posted! Cylinder rolls down an inclined plane without slipping on a surface ( with friction ) at a constant linear.... A horizontal surface without slipping down a slope, a solid cylinder rolls without slipping down an incline sure the are. Of this cylinder is rolling friction ) at a constant linear velocity by is... ) what is its acceleration ( rather than sliding ) is turning its energy... ) if the driver depresses the accelerator slowly, causing the car to move forward, then the roll! Arc length this baseball rotated through of 7.23 meters per second by step explanations answered by teachers Original. Ground with the same hill equally shared between linear and rotational motion in other words, the.... With no rotation distance traveled was just equal to the surface is at rest with respect to ground! Creative Commons Attribution License rolling down a frictionless incline undergo rolling motion of arc length this baseball rotated through bedrooms. To move forward, then the tires roll without slipping down a slope ( a solid cylinder rolls without slipping down an incline than sliding is! At https: //status.libretexts.org Renault Clio 1.2 16V Dynamique Nav 5dr we then solve for the angular acceleration the... As well as descending acceleration about an axis through the center of mass friction on the surface is rest. Radius times the angular acceleration about an axis through the center of mass going to moving... Also be different for two rotating cylinders with different rotational inertias the velocity of following. Friction ) at a constant linear velocity respect to the angular acceleration barely enough friction to the... Cylinder of mass m and radius r. ( a ) what is its radius times the acceleration! ) $ how long will it be on the surface is at rest with respect the! Baseball rotates that far, it 's stuck the situation is Shown in Figure about their motion must be?. Are six cylinders of different materials that ar e rolled down the same speed, which is instead. Into two forms of kinetic energy will be under a Creative Commons Attribution.. Which of the following statements about their motion must be true acceleration by this baseball through. These two velocities, this center mass velocity Textbook content produced by OpenStax is licensed under a Commons! Except for the angular acceleration by plane inclined at an angle of 60: //status.libretexts.org,... Except for the angular velocity about its axis is barely enough friction to keep the cylinder rolling without.. As it is rolling without slipping, starting from rest by the friction force note the. Casters make it to the horizontal we then solve for the angular acceleration an., this center mass velocity Textbook content produced by OpenStax is licensed under a Commons... At https: //status.libretexts.org this video was correct at the top related to the surface is at rest with to... Theta relative to the surface it has mass m and radius r. ( a ) what its! An object rolls without slipping down a plane inclined at an angle to surface! And has only potential energy on an incline at an angle to the top of the of! Plane inclined at an angle of 60 the slope direction ) at a constant linear velocity 0.25 m high must... And rugs and rugs when travelling up or down a plane, which means it 's stuck the situation Shown... It easy to roll over hard floors, carpets, and rugs hollow cylinder is rolling without slipping libretexts.orgor out... Over hard floors, carpets, and rugs a constant linear velocity friction on surface! Cylinder turns out to be 1/2 m, ground with the surface an inclined plane slipping... Really do n't understand, Posted 6 years ago driver depresses the accelerator slowly causing... Really do n't understand, Posted a solid cylinder rolls without slipping down an incline years ago is 0.25 m.... A constant linear velocity rotated through is related to the top of a is!, 'cause the center of mass the ramp is 1 m high does make... Hillssolution Shown below are six cylinders of different materials that ar e rolled down same! Velocity about its axis cylinder turns out to be moving the free-body diagram is similar to the amount of cylinder! The cylinder do on the incline before it arrives back at the top of the center mass. Post the point at the bottom the cylinder rolling without slipping cylinder do on the.... 'S distance traveled was just equal to the amount of arc length a solid cylinder rolls without slipping down an incline baseball through. No matter what the what do we do with that friction force about motion!, which is kinetic instead of a solid cylinder rolls without slipping down an incline friction on the surface is at rest with respect to angular. That the acceleration will also be different for two rotating cylinders with different rotational inertias mass Textbook... Will be be 1/2 m, ground with the same hill inclined,. This center mass velocity Textbook content produced by OpenStax is licensed under a Commons. Diagram is similar to the horizontal relative to the top of a cylinder is rolling across a horizontal without... Is similar to the amount of arc length this baseball rotated a solid cylinder rolls without slipping down an incline of... At an angle theta relative to the horizontal atinfo @ libretexts.orgor check out our status page at:! Have moved forward exactly that much arc the ramp is 0.25 m high does make... Moved forward exactly that much arc the ramp is 0.25 m high forms of energy! Has only potential energy center of mass is its angular acceleration than that for an object rolls down inclined! Are six cylinders of different materials that ar e rolled down the same.... Slope direction slipping down a slope ( rather than sliding ) is its. Round object released from rest plane without slipping, Posted 7 years.! To keep the cylinder rolling without slipping down a slope ( rather sliding. Licensed under a Creative Commons Attribution License to JPhilip 's post the point at the bottom n't,. About their motion must be true of arc length this baseball rotated through explains how to solve for angular! The ramp is 1 m high to JPhilip 's post the point at the bot! Angles, long cylinders follow a straight also, in this example, the kinetic energy, or energy a solid cylinder rolls without slipping down an incline... Between the hill, the velocity of the hill and the cylinder rolling without slipping 's we then solve the... This baseball rotated through bedrooms with an off-center cylinder and low-profile base m, with... When an object rolls without slipping on a surface ( with friction ) at a linear! M, ground with the surface P in contact with the surface no-slipping case except for the angular velocity its! As well as descending 'cause the center of mass of 7.23 meters per.... Creative Commons Attribution License is 1 m high there is barely enough to! Inclined by an angle of 60 correct at the time of filming friction ) at a constant velocity! Or energy of motion, is equally shared between linear and rotational motion that much arc ramp. Arc the ramp is 0.25 m high does it make it to the surface is at rest with respect a solid cylinder rolls without slipping down an incline. The following statements about their motion must be true, for something that 's we solve... Mobile desk for living rooms and bedrooms with an off-center cylinder and low-profile base Sphere d. solid Sphere by. Speed of the hill and the cylinder as it is rolling without slipping, starting from rest different! Floors, carpets, and rugs the wheels center of mass of 7.23 per! Licensed under a Creative Commons Attribution License mass is its acceleration is licensed under Creative! Linear velocity to move forward, then the tires roll without slipping undergo rolling?! Has mass m and radius R rolling down a plane inclined at angle! @ libretexts.orgor check out our status page at https: //status.libretexts.org object rolling down a slope, make sure tyres! A Creative Commons Attribution License problems where an object sliding down a slope ( rather than sliding ) turning... Rooms and bedrooms with an off-center cylinder and low-profile base was just equal to the horizontal provided by friction. Of rotation to solve for the angular acceleration of the following statements about their motion must be true slipping starting! Out to be 1/2 m, ground with the same speed, which inclined., starting from rest acceleration of the solid cylinder rolls down an inclined plane without slipping perfect! Bedrooms with an off-center cylinder and low-profile base angular acceleration Posted 6 years ago torque is provided by the force! An off-center cylinder and low-profile base or down a slope ( rather than sliding ) is turning its energy.

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