Question

A mass is revolving around a circle that is in the plane of the paper. Then find the direction of angular acceleration
A. Perpendicular to the plane of the paper
B. Towards the radius
C. Tangential
D. At right angle to angular velocity

Answer 1

Hint: Before we start addressing the problem, we need to know about torque and angular acceleration. When a force is applied to a body, and the force causes a rotational motion in the body, that force is known as torque. Angular acceleration is defined as the rate of change of angular velocity and is usually expressed in radians per second per second.

Complete step by step solution:
We know that force is responsible for linear motion and torque is responsible for rotational or angular motion. Here we have considered that a man is revolving around a circle which is in a plane of the paper. The torque is responsible for this motion and the value of the torque is calculated by the formula.
\[\tau = I\alpha \]
where \[\alpha \] is the angular acceleration, which means the direction of the torque is similar to that of the direction of \[\alpha \].

Then the direction of torque can be written as \[\overrightarrow \tau = \overrightarrow r \times \overrightarrow F \]implies the torque is perpendicular to \[\overrightarrow r \] and \[\overrightarrow F \]. Since it is perpendicular to torque, the \[\overrightarrow r \] and \[\overrightarrow F \] are perpendicular to each other. Then, the torque is perpendicular to the plane of paper then the angular acceleration is also perpendicular to the plane.

Hence, option A is the correct answer.

Note:The direction of the angular acceleration can be determined using the right-hand thumb rule whether it is clockwise or anticlockwise in direction.