First slide

Torque

Question

A sphere is spinning about a diameter and its angular momentum is varying with time according to the graph shown in figure. If moment of inertia of the sphere is 2 Kg-m², its maximum angular acceleration is

Moderate

A

4 rad/s²
B

2 rad/s²
C

zero
D

0.5 rad/s²

Solution

Since $τ = \frac{d L}{d t},$ no torque is acting on the sphere in the interval t = 2s to t = 4s and torque acting on the sphere in the interval t = 0 to t = 2s = slope of L - t graph
$\Rightarrow τ = \frac{8}{2} N - m = 4 N - m$
$∴ {(α)}_{\max} = \frac{τ}{I} = \frac{4}{2} r a d / s^{2} = 2 r a d / s^{2}$

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