Question

A dog of mass m is walking on a pivoted disc of radius R and mass M in a circle of radius R/2 with an angular frequency 'n' . The disc will revolve in the opposite direction with frequency :
A) mn/M
B) mn/2M
C) 2mn/M
D)2Mn/M

Answer 1

The direction of angular frequency is ω = m / 2Mn

Explanation:

• Angular momentum of the system should be zero.

Moment of inertial of the dog is m(R^2)^2 (since dog is moving in radius R / 2)  Angular velocity is n.

Angular momentum is L= Iω = mR^2 / 4n

Now the moment of inertia of the disc is 1 / 2MR^2.

Suppose the disc is rotating with a angular velocity "ω".

Therefore angular momentum is 1 / 2MR^2ω.

Thus

1 / 2MR^2ω = 1/4mR^2n

ω = m / 2Mn

Thus the direction of angular frequency is ω = m / 2Mn

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