Question

Uniform circular motion is an accelerated motion. Explain it.

Answer 1

Hint: In the accelerated motion, the velocity of the body changes at each point. In uniform circular motion, only the magnitude of velocity that is speed remains constant. Recall the force responsible for the circular motion of the body. Express the acceleration of that force.

Complete answer:
We know that in accelerated motion, the velocity of the body changes at each point. In case of linear motion of the body when the velocity of the body is not changing, there will not be any acceleration of that body.

In case of uniform circular motion, we know that the speed which is a scalar quantity does not change at any point but the velocity of the body which is a vector quantity, changes with change in direction at each point.

The velocity of the body in the circular motion is tangent to the path at each point. Since the direction of motion of the body in a circular motion is tangent to the path, we can say that the velocity of the body changes with the direction of motion and both have the same direction.

In uniform circular motion, the acceleration is along the radius towards the centre of the circular motion. Since the velocity change is linear, the uniform circular motion is uniformly accelerated motion.

Note:Students can answer this question in a different way by comparing the linear motion and uniform circular motion. In linear motion, if the velocity of the body remains constant, there is no change in linear momentum of the body. Since the linear momentum remains constant, according to Newton’s second law, the force acting on the body is zero. But in case of circular motion, the force responsible for the circular motion is centripetal force whose acceleration is given as, $$a={\displaystyle \frac{v^2}{r}}$$, where, v is the velocity and r is the radius of circular motion. If the acceleration is zero, the centripetal force would be zero and the body will not have uniform circular motion at all.