## The Centripetal Force Requirement

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. Because of this direction change, you can be certain that an object undergoing circular motion is accelerating (even if it is moving at constant speed). And in accord with Newton's laws of motion, an accelerating object must be acted upon by an unbalanced force. This unbalanced force is in the same direction as the direction of the acceleration. For objects in uniform circular motion, the net force and subsequent acceleration is directed inwards. Circular motion requires a net inward or "centripetal" force.

Without a net centripetal force, an object cannot travel in circular motion. In fact, if the forces are balanced, then an object in motion continues in motion in a straight line at constant speed. This can be demonstrated by carrying a tennis ball upon a flat, level board. Once the tennis ball and the board are in motion, they will continue in motion in the same direction at the same speed unless acted upon by an unbalanced force. This demonstrates Newton's first law of motion. But if an unbalanced force is applied to the flat board, then the flat board will accelerate. If the force is continually directed towards a point at the center of the circle, then the flat board will round the corner in a circular-like path. The ball on the other hand will continue to move in the same direction since there is no unbalanced force acting upon it. The board will move out from under the tennis ball. This is illustrated in the animation on the left below.

Now if a block is secured to the board in such a manner that the block applies an unbalanced force to the ball that is directed towards the center of the circle, then quite another phenomenon will be observed. With the block providing a normal force directed inward, the ball can round the corner in a circular-like path. The block supplies the centripetal force required for circular motion. With the centripetal motion requirement met, uniform circular motion can occur. This is illustrated in the animation on the right.

 Without a centripetal force, an object in motion continues along a straight-line path. With a centripetal force, an object in motion will be accelerated and change its direction. The tendency of a moving object to continue in a straight line in the absence of an unbalanced force and to turn in a circle in the presence of a inward-directed force (i.e., centripetal force) is a common experience as a passenger in an automobile. When the car makes a sudden turn, the passengers tend to continue in their straight line path. This straight line motion continues until the presence of a side door or another passenger pushes upon the passenger in order to accelerate him/her towards the center of the turn. The force experienced by the passenger is an inward force; without it, the passenger would slide out of the car.

For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. Specific information is available about the following topics:

Velocity

Acceleration

Net Force and Acceleration

Newton's Law of Inertia

Circular Motion and Tangential Velocity

Circular Motion and Acceleration

The Centripetal Force Requirement