Question

A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant?

• A. Centripetal acceleration
• B. Tangential acceleration
• C. Angular acceleration
• D. None of these

Answer 1

The correct option is C

Angular acceleration

Explanation for correct options,

In the case of option B,

1. Tangential acceleration is the acceleration of a particle in direction of its velocity or in direction of motion which contributes to increasing or decreasing the velocity.
2. A particle is revolving in a circle of radius $R$ with increasing its speed uniformly.
3. Since the angular velocity is increasing uniformly hence the tangential acceleration is constant, $\frac{dw}{dt}=a_t$, $a_t$ is constant
4. $a_t=\alpha r$, $\alpha$ is the angular acceleration
5. Hence option B is correct.

In the case of option C,

1. Angular Acceleration is defined as the time rate of change of angular velocity.
2. We can write Angular acceleration in terms of tangential acceleration, $\alpha =\frac{a_t}{R}$, $a_t$ is the tangential acceleration, $R$ is the radius.
3. As $a_t$ is constant, $\alpha$ will also be constant.
4. It is usually expressed in radians per second per second.
5. $\alpha =\frac{d\omega }{dt}$Hence, angular acceleration is constant.

Explanation for incorrect options,

In the case of option A,

1. Centripetal acceleration is defined as the rate of change of tangential velocity.
2. Centripetal acceleration changes with direction,$a_c=\frac{v^2}{R}$,$v$ is the velocity of the particle.
3. As $v$ is increasing so it is not constant.
4. Hence option A is incorrect.

In the case of option D,

1. We can see when a particle is revolving in a circle by increasing its speed uniformly, angular acceleration and tangential acceleration remain constant
2. Hence option D is incorrect.

Hence, options B and C are the correct answers.