Question

A disc of radius R is rotating with an angular speed ω_o about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is μ_k.

(a) What was the velocity of its centre of mass before being brought in contact with the table? 

(b) What happens to the linear velocity of a point on its rim when placed in contact with the table? 

(c) What happens to the linear speed of the centre of mass when disc is placed in contact with the table? 

(d) Which force is responsible for the effects in (b) and (c). 

(e) What condition should be satisfied for rolling to begin? 

(f ) Calculate the time taken for the rolling to begin.

Answer 1

(a) Zero 

(b) Decreases 

(c) Increases 

(d) Friction

(e) v_cm = Rω

(f) Acceleration produced in centre of mass due to friction:

Angular acceleration produced by the torque due to friction,

For rolling without slipping,