# Why does an object in circular motion stay in a circle?

My doubt is that in an ideal condition where an object is in uniform circular motion, only centripetal force is acting towards the centre. Why wouldn't an object move towards the centre when centripetal acceleration is towards there?

I felt that since centripetal force is perpendicular to velocity of the object in circular motion, no work is done. And if this is true then what about a horizontal projectile? In that case, we give a velocity along the $$x$$ direction as we throw it from a certain height. Here also velocity is perpendicular to gravitational force, but still kinetic energy changes.

• When you throw something horizontally, very quickly the force is no longer perpendicular Commented Sep 4, 2023 at 10:45

Work done is the product of force x distance moved in the direction of the force. Since an object moving in a circle never gets closer to or more distant from the center, it never moves in the direction of the force, so no work is done.

In the case of a horizontally thrown object the object does move in the direction of the force due to gravity if it falls. The gravitational force is only perpendicular to the direction of movement at the instant it is released, after which the object begins to move in the direction of the force and gravitational potential energy is converted to vertical kinetic energy downwards. The horizontal velocity will not be changed.

In the case where an object is moving in a circular orbit around the source of the gravitation force, the object is being accelerated towards the center of force at exactly the right rate to keep it from flying away or falling closer. The F = ma law applies to it. It's just that the acceleration it experiences is exactly enough to change its direction without changing it's speed.

Since the object never actually moves in the direction of the applied force, no work is done, although the velocity is constantly changing direction.

The problem appears when we look at centripetal force after assuming the object in a circular motion. But the actual case is that the object is in circular motion because of the centripetal force otherwise the Newton's First law applies i.e., the object can't change its direction until an external force is applied.

I hope it helps!

• -1 because this doesn't answer the question, just says "the object is in circular motion because of the centripetal force". Commented Sep 5, 2023 at 18:33
• @Kotlopou agree, but it clears the concept and there is nothing hard to analyse the problem further.
– D13G
Commented Sep 5, 2023 at 19:52