Question

Prove the relation τ = /α for a rigid body rotating about a fixed axis?
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Answer 1

In continuation to the pic....

€τ= 0

ie, for rational equilibrium total external torque acting on the body be zero.

Eqn of motion of a rotating body is given by

τ=€τ=dL/dt

For body in rotational equilibrium,

τ =0

dL/dt=0

or L = constant

ie, angular momentum of body in rotational equilibrium will stay constant.

Therefore, τ=Iα

Hence, proved.

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