A cylinder rolls up an inclined plane to a ce | vedclass

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(B) When the cylinder rolls up the inclined plane,its linear velocity $v$ is directed up the incline and its angular velocity $\omega$ is clockwise. S

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Up the incline in both upward and downward motion.

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(B) When the cylinder rolls up the inclined plane,its linear velocity $v$ is directed up the incline and its angular velocity $\omega$ is clockwise. Since it is moving up,its linear velocity decreases,meaning it experiences a linear deceleration. To maintain rolling without slipping,it requires an angular deceleration. The torque provided by the frictional force $f$ acting up the incline creates a counter-clockwise torque,which provides the necessary angular deceleration.When the cylinder rolls down the inclined plane,its linear velocity $v$ is directed down the incline and its angular velocity $\omega$ is counter-clockwise. As it moves down,its linear velocity increases,meaning it experiences linear acceleration. To maintain rolling without slipping,it requires an angular acceleration. The frictional force $f$ acting up the incline creates a torque that results in the necessary angular acceleration to increase the counter-clockwise angular velocity.

$A$ cylinder rolls up an inclined plane to a certain height and then rolls down. (During these motions,the cylinder rolls without slipping). What are the directions of the frictional force acting on the cylinder?

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