Uniform Circular Motion

What is uniform circular motion?

When an object moves in a circular pattern with a constant velocity ($v$). Additionally, although $v$ is constant, its direction changes continuously.

Does acceleration change in uniform circular motion?

Yes. Because $a$ is defined as a velocity per unit time and the direction of velocity changes, acceleration changes constantly in uniform circular motion. In fact, a uniformly circularly moving object is accelerating constantly towards the center, i.e. centripetal acceleration or radial acceleration.

How can centripetal acceleration ($a_{C}$) be calculated?

$$a_{C} = \frac{v^{2}}{r}$$ (62.1)

Again, the vector of acceleration is towards the center of the orbit. If you had a bird's eye vantage point of an orbiting object, this would make sense: The spinning object is always coming around `back' towards its axis of rotation.

What force keeps a rotating object moving about a fixed axis?

Centripetal force, an application of Newton's second law of motion (see page for a review of Newton's second law):

$$\Sigma F_{R} = ma_{R}=m\frac{v^{2}}{r}$$ (62.2)

What counters centripetal force?

The force exerted by the object holding the spinning object, e.g. the force your hand exerts on a spinning ball on a string.

What trajectory does a spinning object follow if released?

The velocity vector, i.e. a direction tangential to the orbit: Think of a softball pitcher and the direction the softball travels once the ball is released.