Question

A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10π rad s^-1 . Which of the two will start to roll earlier? The co-efficient of kinetic friction is μ_k = 0.2.

Answer 1

Motion of the two objects is caused by frictional force. As per Newton’s second law of motion, we have frictional force, f = ma μkmg= ma Where, a = Acceleration

produced in the objects m = Mass a = μ_kg … (i)

As per the first equation of motion, the final velocity of the objects can be obtained as:

The torque applied by the frictional force will act in perpendicularly outward direction and cause reduction in the initial angular speed.

Torque, τ= –Iα

α = Angular acceleration 

μ_xmgr = –Iα

a = (-μ_xmgr)/l  ................(iii)

Using the first equation of rotational motion to obtain the final angular speed:

Since t_d > t_r, the disc will start rolling before the ring.