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A hoop of radius r and mass m rotating with an angular velocity ω is placed on a rough horizontal surface The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip ?

A hoop of radius r and mass m rotating with an angular velocity ω is placed on a rough horizontal surface The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip ?

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2 Answers

Gaurav Gupta
askIITians Faculty 686 Points
6 years ago
564-1214_mvr.JPG
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
Let us consider a point ‘A’ on the ground.
Now, the only force acting on the body will be the force of friction whose torque about A is zero.
Hence, Angular momentum about A is conserved.
→ Iw = Iw’ + mvr
where, v = w’r (for pure rolling)
or, w’ = v/r; also I = mr2
Hence, mr2w = mr2v/r + mvr
or, r2w = 2vr
Therefore, v = wr/2
 
Hope it helps.
Thanks and regards,
Kushagra
 

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