Question

How does torque affect angular momentum?

Answer 1

Hint: In order to see what effect does torque have on angular momentum of a body, we must understand what torque is. In physics and mechanics torque which is also termed as moment of force is the tendency of a force to rotate the body on which the force is applied. In other words, one could say that torque is the rotational equivalent of force.

Complete answer:
Now, angular momentum is a vector quantity that is a measure of the rotational momentum of a rotating body or system. It is analogous to linear momentum and is given as a product of moment of inertia of the body and its angular velocity.
A torque applied on a body can cause its angular momentum to increase, decrease or change its direction. This can be explained by the causality in the torque equation. The torque equation equivalent of Newton’s Second Law of motion can be given as:
$\Rightarrow \overrightarrow{r}\times \overrightarrow{F}={\displaystyle \frac{d\overrightarrow{L}}{dt}}$ where, $(\overrightarrow{r}\times \overrightarrow{F})$ is the value of torque applied.
Here, F is the applied force at a distance (r) from the axis of rotation of the object.
Now, let the initial angular momentum be L1 and final angular momentum be L2. Then, we can have three cases for the change in angular momentum of the object:
Case 1:
When the applied torque is in the direction of initial angular momentum. This results in an increase in the angular momentum of the body without changing its direction. Hence,
$\Rightarrow L_2>L_1$
Case 2:
When the applied torque is in the direction opposite to the initial angular momentum. This results in a decrease in the angular momentum of the body without changing its direction. Hence,
$\Rightarrow L_2<L_1$
Case 3:
When the applied torque is in the direction different to the initial angular momentum. This results in a change in direction of the angular momentum of the body.

Note:
An interesting case of application of torque in changing angular momentum is, when we pedal our bicycle, in the beginning we have to accelerate the bicycle. But after a certain time, even though we keep pedaling a bicycle, the wheels move with a constant angular velocity. This is because an equal amount of angular momentum is applied on the wheel by friction at the surface of contact. These two torques balance each other out and our bicycle moves with a constant velocity.