Question

Torque (t) acting on a body in the interval 0 to T seconds is shown in figure. Angular impluse on the body in this interval is​

Answer 1

answer : $\frac{\tau_0 T}{2}$

explanation : torque is the rate of change of linear momentum per unit time.

i.e., $\tau=\frac{dL}{dt}$

or, $\int\limits^{t_2}_{t_1}{\tau}\,dt=\int\limits^{L_2}_{L_1}\,dL$

means, area under the torque - time graph = change in angular momentum.

we also know, change in angular momentum is nothing but angular impulse during that time.

so, angular impulse = area under the torque time graph

see figure, it looks like a triangle of base = T and altitude = $\tau_0$

so, area of triangle = 1/2 × base × altitude = 1/2 $T\tau_0$

hence, angular impulse = $\frac{\tau_0 T}{2}$