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Asked by Gurpreet Last Modified
Answer 
Tasneem
Disc
Radii of the ring and the disc, r = 10 cm = 0.1 m
Initial angular speed, ω0 =10 π rad s–1
Coefficient of kinetic friction, μk = 0.2
Initial velocity of both the objects, u = 0
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 = μkg … (i)
As per the first equation of motion, the final velocity of the objects can be obtained as:
v = u + at
= 0 + μkgt
= μkgt … (ii)
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
μxmgr = –Iα
Using the first equation of rotational motion to obtain the final angular speed:
Rolling starts when linear velocity, v = rω
Equating equations (ii) and (v), we get:
Since td > tr, the disc will start rolling before the ring.
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