Question

A motor cyclist going round in a circular track at constant speed has__
A. Constant linear velocity
B. Constant acceleration
C. Constant angular velocity
D. constant

Answer 1

Hint: As per question if a motorcyclist is moving round with constant speed in a circular track what will be its linear velocity, linear acceleration, force and angular velocity. As we know that speed is a scalar quantity and thus does not depend on the direction of the body so in circular motion speed can be constant but in a circular path body needs to change its direction, force changes but angle remains the same as body is moving with same speed.

Formula used:
Angular velocity $\omega =\dfrac{\Delta \theta }{\Delta t}$
Linear velocity $v=\dfrac{\Delta s}{\Delta t}$
Linear displacement = arc/radius=$\theta =\dfrac{s}{r}$

Complete step by step solution:
Precise speed relies on Angular acceleration of any body for a specific axis. So, for a specific axis of rotation, angular acceleration must be zero for uniform angular velocity. If we change the axis of the body obviously the linear velocity of the body will change (Since $\omega =\dfrac{v}{r}$) because radius will also change. This will particularly affect angular velocity ($\omega $).

Since the object's velocity vector is continually taking a different path, the moving article is going through a speed increase by a centripetal force toward the centre point of pivot. Without this velocity increase, the object would move in an orderly straight line as per Newton's laws of motion.

Hence, the correct option is C.

Note: As body is moving with the constant speed (not depend on direction) in a circular motion means body is covering equal distance in equal interval of time () whereas velocity which is a vector quantity so this will not remain constant while body moving in circular motion because body changes direction while circulating. Also linear acceleration (linear velocity/time) will also change with change with linear velocity. But angular acceleration which is defined as the angle covered with time so as the body is covering equal distance in circular motion so it will also cover equal angle in equal interval of time thus angular velocity is constant. Whereas force (ma) on the body will also not be constant as it will change with linear acceleration.