Question

If there is a change of angular momentum from 1J to 5J in 5 seconds. Then the torque is:
A) \[\dfrac{{3J}}{5}\]
B) \[\dfrac{{4J}}{5}\]
C) \[\dfrac{{5J}}{4}\]
D) None of these

Answer 1

Hint: Change in angular momentum is given and the time period is given. Recall the definition of torque. Torque is defined as the rate of change of angular momentum. Substitute the values accordingly to find the answer.

Complete step by step solution:
As we know force is defined as the rate of change of linear momentum. Here, rate of change means changes in linear momentum divided by time period. Where linear momentum is the product of mass of an object and the velocity by which the object is moving. Force is responsible for the linear motion.

Similar to force, we have Torque for rotational motions. In rotational motion, we have angular momentum. Torque is defined as the rate of change in angular momentum divided by the time period. Where angular momentum is the product of angular momentum and the distance of an object from a rotational axis.

In linear motion, when no external force is acting on the system then the linear momentum of the system is conserved. Similarly, in rotational motion, when no external torque is acting on the system, the angular momentum is conserved.
Mathematically, from the above discussion we can achieve:
\[\tau = \dfrac{{dL}}{{dt}} = \dfrac{{\Delta L}}{{\Delta t}}\]
Where $\tau $ is the torque
\[dL,\Delta L\] is the change in angular momentum
\[dt,\Delta t\] is the change in time
\[ \Rightarrow \tau = \dfrac{{5J - 1J}}{5}\]
\[ \Rightarrow \tau = \dfrac{4}{5}\] Joules.

Therefore, the torque is \[\tau = \dfrac{4}{5}\] Joules. Hence, option (B) is the correct option.

Note: Remember that torque is equivalent of force. Force is a term used for linear motion while torque is a term related to rotational motion. Also remember, if torque is acting on any system then that system is performing rotational motion. Torque has the same units as work done.