1. Circular Motion
An object that revolves about a single axis undergoes circular motion.
The axis of rotation is the line about which the rotation occurs.
Tangential speed (vt) describes the speed of an object in circular motion. It depends on the distance from the object to the center of the circular path.
Ex: merry-go-rounds, carousel horses,
amusement park rides – the outside
object has a greater tangential speed.

2. Circular Motion
When the tangential speed is constant, the motion is described as uniform circular motion.
So when an object is moving in circular motion, even if the tangential speed is constant, the object is accelerating.
The object is accelerating because it is constantly changing direction.

3. Circular Motion
The acceleration of an object in circular motion is called centripetal acceleration (ac).
Centripetal acceleration = (tangential speed) radius of circular path
ac = vt2/r
The direction of centripetal acceleration is towards the center of the circle.

4. Circular Motion
Ex: A car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed? G: r = 48.2 m S: 8.05 m/s2 = vt2/48.2 m ac = 8.05 m/s2 S: vt = 19.7 m/s U: vt E: ac = vt2/r

5. Circular Motion
The inertia of an object traveling in a circular which pulls the object into continuing in a straight line path. However there are forces acting on the object as it moves around.
Centripetal force (Fc) is the net force that is directed toward the center of the circle. It is in the same direction as the centripetal acceleration.
Centripetal force is the net force towards the center of the circular path followed by an object moving in uniform circular motion.
Ex: this can be the force of a string on a rotating ball, the gravitational force keeping the moon in orbit, or the friction between a racecar’s tires and the track

6. Circular Motion
Centripetal force is necessary for circular motion – the force changes the direction of the velocity. If there were no centripetal force, the object would continue on a straight line path that is tangent to the circle.

7. Circular Motion
Fc = mac So therefore: Fc = mvt2/r Centripetal force= mass x (tangential speed)2 radius of circular path

8. Circular Motion
Ex: A pilot is flying a small plane at 56.6 m/s in a circular path with a radius of m. The centripetal force needed to maintain the plane’s circular motion is 1.89 x 104 N. What is the plane’s mass? G: vt = 56.6 m/s S: m = Fcr/vt2 r = m m = [(1.89 x 104 N)(188.5 m)] Fc = 1.89 x 104 N (56.6 m/s)2 U: m S: m = 1110 kg E: Fc = mvt2/r