Question

Is the acceleration of a particle in uniform circular motion constant or variable?

Answer 1

Hint:The uniform circular motion is the motion of the body in which the body moves in the circle with constant speed. In uniform circular motion, the velocity vector changes at every instant of time. Recall the expression for the acceleration in the circular motion to answer this question.

Complete answer:
We know that the uniform circular motion is the motion of the body in which the body moves in the circle with constant speed. In a linear motion, if the velocity of the body does not change, we can say that the body is in uniform motion. But this is not the case in uniform circular motion.

In uniform circular motion, the velocity vector changes at every instant of time, that is the direction of the velocity changes since it is tangent to the path. The circular motion is caused by the centripetal acceleration whose direction is towards the centre of the circular motion. We know the centripetal acceleration is given by the relation,
\[{\vec a_C} = \dfrac{{{{\vec v}^2}}}{r}\]
Here, v is the velocity of the body and r is the radius of the circular motion.

The radius of the circular motion remains the same at every instant of time. Since the velocity vector changes with time, we can say that the acceleration also changes with time.

Therefore, the acceleration in the uniform circular motion is variable.

Note: If the speed of the body in the circular motion changes with time, then we have to introduce the tangential acceleration term to express the total acceleration in the circular motion. This type of motion is known as non-uniform circular motion. The motion of the planets around the sun is non-uniform since their speeds change at every instant.