Question

The angular acceleration of a body, moving along the circumference of a circle, is:

• A. along the axis of rotation
• B. along the radius, away from center
• C. along the radius towards the centre
• D. along the tangent to its position

Answer 1

The Correct Option is D

To understand the direction of angular acceleration for a body moving along the circumference of a circle, let's consider the fundamental concepts of circular motion and angular acceleration.

Angular acceleration is defined as the rate of change of angular velocity. When an object moves along a circular path, its tangential velocity changes, leading to tangential acceleration. This change in velocity along the tangent of the circle results in angular acceleration.

In circular motion, there are two important accelerations to consider:

• Centripetal (radial) acceleration: Directed towards the center of the circle; responsible for changing the direction of velocity.
• Tangential acceleration: Directed along the tangent to the circle; responsible for changing the magnitude of velocity (speed).

Angular acceleration specifically refers to tangential acceleration, as it is associated with the rate at which the angular speed changes. Hence, the angular acceleration is along the tangent to the position of the body on the circular path.

Let's now analyze and rule out other options:

• Along the axis of rotation: This relates more to the rotational axis itself and not the tangential or circular motion of the body. It does not describe the direction of angular acceleration.
• Along the radius, away from center: This describes a radial component, which in circular motion is centripetal, acting towards the center, and not indicative of angular acceleration.
• Along the radius towards the center: This is the direction of centripetal (radial) acceleration, which influences the circular path but does not correspond to angular acceleration.

Thus, the correct answer is that angular acceleration is along the tangent to its position.