Question

Find the time when a disc will start pure rolling

Answer 1

Answer:

Friction acts in backward direction (opposite to velocity) to change the direction of rotation. First, the angular velocity and linear velocity decreases. Then the angular velocity becomes zero but the sphere still has a velocity. Then the angular velocity increases in opposite directions till ω = v / R ω=v/R f = μ m g f=μmg α = 5 μ g 2 R α=5μg2R a = μ g a=μg Time taken for angular velocity to become zero t 0 = v 0 5 μ g t0=v05μg Velocity at t 0 t0 is v = 4 v 0 5 v=4v05 After that, ω ω increases from 0 to v / R v/R 4 v 0 5 R − μ g t R = 5 μ g 2 R t 4v05R−μgtR=5μg2Rt This gives t = 8 v 0 35 μ g t=8v035μg which is incorrect.