Question

Relation between torque and angular momentum is similar to the relation between
A. Energy and displacement
B. Acceleration and velocity
C. Mass and moment of inertia
D. Force and linear momentum

Answer 1

Hint: In these types of questions remember to formulate the relation of $$\mathrm{T}={\displaystyle \frac{dl}{dt}}$$ and $F={\displaystyle \frac{dp}{dt}}$where P is the linear momentum and L is the angular momentum. Using these relations, find the direct relation between torque and angular momentum which will lead you to the answer.

Complete Step-by-Step solution:
Angular momentum is described as: L=$i\omega$
Here it is a moment of inertia and $\omega$ is omega.
On the other hand we can describe torque as a twisting force that causes rotation. Torque is a force multiplied by radius multiplied by the sine of angle ($\theta$) at which force is applied.
$T=4\sin \theta$
So, torque is directly affecting the angular velocity of a spinning object. Since torque can change angular velocity, and the amount of angular momentum an object has depends on its angular velocity, it makes sense that torque can change angular momentum this is how the two are related.
The expression for angular momentum and torque is:${\displaystyle \frac{dl}{dt}}$
Thus, the relation between angular momentum and torque is the same as between the linear momentum and force. There is an analogy between parameters of linear motion and rotational motion.

Note: You must have noticed that the faster you spin the longer it takes you to stop. This is due to the Angular Momentum. The more angular momentum the object has, the more it tends to keep rotating. Angular momentum can be defined as the moment of inertia time’s angular velocity.