UNIFORM CIRCULAR MOTION

TargetTo define period, frequency, uniform circular motion, centripetal acceleration, centripetal force and centrifugal force;

To identify the forces acting on a body moving in a circular path;

TargetTo derive the equation for

centripetal force from Newton’s second law of motion;

To cite applications of centripetal force; and

To solve problems related to circular motion.

Period and Frequency Frequency (f)

is the number of revolutions completed by a body in a given time.

Units: rev/s, rev/min, rev/hr. or rev/yr.

Period (T) is the time required for a body to make one complete revolution.

Units: s, min, hr. or yr.

Uniform Circular Motion

It is the motion of a body that moves in a circular path at constant speed.

Centripetal acceleration

The inward acceleration of a body moving in circular motion.

Forces Centripetal force is the force that pulls a body inward when moving in a circular path.

Centrifugal force is the force that is directed away from the center of a circular path.

Examples

Examples

Equations Period (T)

or

Frequency (f) or

Equations Speed (v)

where: C is the circumference;T is the period;r is the radius; andf is the frequency

Equations Centripetal acceleration (ac)

Centripetal force (Fc)

where: v is the speed;r is the radius; andm is the mass

Sample Problem 1A little girl is playing with her skip

ball. The ball is in uniform circular motion and makes 20 revolutions in 4 s. (a) What is its period? (b) What is its frequency? (c) If the length of the cord that holds the ball is 0.8 m, what is its speed? (d) If the ball’s mass is 3 g, how much force is acting on the ball to keep it in uniform circular motion?

Sample Problem 1Given: no. of rev = 20 time = 4 s lengthcord = 0.8 m mass = 3 gFind:

a. T c. vb. f d. Fc

Sample Problem 2A 0.1-kg mass is attached to a

0.9-m length of string. The weight is swung in a horizontal circle, making one revolution in 1.2 s. (a) Find the speed of the mass. (b) What is its centripetal acceleration? (c) What is the force that the string exerts on it?

Sample Problem 2Given: mass = 0.1 kg lengthstring = 0.9 m no. of rev = 1 time = 1.2 sFind:a. vb. ac

c. Fc