Uniform circular motion requires an acceleration directed towards the center of the circle due to the changing direction of velocity as an object moves at a constant speed in a circle. This centripetal acceleration can be calculated using the object's velocity and the radius of the circle. A centripetal force is also required to provide the necessary centripetal acceleration, and this force can be calculated using the object's mass, velocity, and the radius. Examples of centripetal force include gravity on the moon, friction on car tires, and tension in a swung rope.

1. Mechanics
Topic 2.4 Uniform Circular Motion

2. Circular Motion
A body moving with uniform speed in a
circle is changing velocity as the
direction changes.
This change of velocity, and the
acceleration is directed towards the
centre of the circle
This acceleration is called the
centripetal acceleration

3. Vector Diagrams
velocity at a tangent
uniform speed
Acceleration and
force directed
towards the centre

4. Centripetal Acceleration
The expression for centripetal
acceleration is
a = v2 = 4p2r
r T2
 Where v is the velocity at any instant
(i.e.the constant speed)
 And r is the radius of the circle
 T is the time period of one complete circle

5. Centripetal Force
The expression for centripetal force is
F = mv2
r
 Where v is the velocity at any instant
(i.e.the constant speed)
 m is the mass of the object
 And r is the radius of the circle

6. Examples of Centripetal Force include
 the gravitational force keeping the moon in
its orbit
 the friction acting sideways on the tyres of
a car turning a corner
 the tension in a rope, when a bucket of
water is swung around your head

7. Examples of Centripetal Force include
 the gravitational force keeping the moon in
its orbit
 the friction acting sideways on the tyres of
a car turning a corner
 the tension in a rope, when a bucket of
water is swung around your head