Q7.30 A solid disc and a ring, both of radius are placed on a horizontal table
simultaneously, with initial angular speed equal to . Which of the two will start to roll
earlier ? The co-efficient of kinetic friction is .
Friction is the cause for motion here.
So using Newton's law of motion we can write :
Now by the equation of motion, we can write :
The torque is given by :
Now using the equation of rotational motion we can write :
Condition for rolling is
So we can write :
For ring the moment of inertia is :
So we have :
Now in case of the disc, the moment of inertia is :
Hence disc will start rolling first.
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