Question

Magnitude of angular momentum of a wheel changes from 2L to 3L in 5 sec by a constant torque acting opposite to initial direction of rotation. What is the magnitude of the torque?
(A) \[\dfrac{L}{5}\]
(B) L
(C) \[\dfrac{2L}{5}\]
(D) \[\dfrac{3L}{5}\]

Answer 1

Hint:First of all, let us define what is a moment of force. The moment of force is a measure of the ability of the force acting on a particular body to rotate it around a given axis. Moment of force is called torque.

Complete step by step answer:
Now we know the relationship between torque and angular momentum is given by,
\[\dfrac{dL}{dt}=\tau \],
If \[\tau =0\], this means that angular momentum is constant
Now change in angular momentum is 3L-2L= L
The time taken to bring this change is 5s.
\[\begin{align}
& \Rightarrow \tau =\dfrac{\Delta L}{\Delta t} \\
&\therefore \tau =\dfrac{L}{5} \\
\end{align}\]

So, the correct option is (A).

Additional information:
While calculating torque we have to keep in our mind that it is a vector quantity and is given by the cross product of force acting on the body and the perpendicular distance from the axis of rotation. So, we have to consider the angle between the two vectors.

Note:Although the torque is given by the differential of angular momentum with the time but if the time interval is large, we can write it in the form of delta. Delta is used when the change is large and differential is used when the change is infinitesimally small. Torque is nothing but a force which acts on a body and the body starts rotating about an axis of rotation.