Question

A uniform cylinder of radius r is spinned to an angular velocity 0and then placed on an incline for which coefficient of friction is = tan . ( is the angle of incline). The centre of mass of the cylinder will remain stationary for time

Answer 1

Explanation:

Given A uniform cylinder of radius r is spinned to an angular velocity 0 and then placed on an incline for which coefficient of friction is = tan . ( is the angle of incline). The centre of mass of the cylinder will remain stationary for time

• A uniform cylinder of radius r is spinned to an angular velocity ωo and we need to find the time the centre of mass of cylinder will remain at rest.
• The cylinder is rotating in clockwise direction. Now there will be friction of torque in anticlockwise direction. Hence ωo = 0. At the time of rest when there is no rotation there will be static friction.
• So now force of friction will be
•                                    So mg sin theta R = mR^2 / 2 α
•                                          Or g sin theta = R / 2 α
•                                         Or α = 2g sin theta / R
•      So this will be in anticlockwise direction.
• So if we consider the clockwise direction to be positive,
•      Then α = - 2g sin theta / R
•     Now ω final = ω initial + α t
•                          = ωo – 2g sin theta / R t
•    Therefore t = ωo R / 2g sin theta
• so in this time the centre of mass will be at rest

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https://brainly.in/question/1705360