Download Uniform Circular Motion (UCM)

Uniform Circular Motion (UCM)
Review Questions:

What are Newton’s first two laws of motion?

What does acceleration mean?

What happens to objects when they accelerate?

What causes objects to accelerate?

What would a moving object do if the forces acting on it were balanced?
Uniform Circular Motion (UCM) occurs when an object moves at constant speed in a circular
pathway. The speed remains constant, but the velocity does not, because the object's direction is
always changing (velocity = speed + direction) . Since the direction component of velocity is
changing as the object moves in a circle, the object is accelerating. It is called centripetal acceleration
(ac), and it measures how quickly the object is changing direction.

What causes an object to accelerate???
The unbalanced force (net force) that causes objects to move in a circle is called the centripetal force
(FC). The centripetal force is provided by a real force acting on the object, and it pulls or pushes the
object toward the center of the circular pathway. The Fc is provided by a real actual force that must
be identified for each situation. Fc can be provided by Force of tension (F T), Force of Friction (Ff),
Normal Force (FN), or Force of gravity (weight) (Fg).

A ball is whirled in a circle on the end of a string. Which direction will the ball go if the string is
let go?
The direction of the velocity of an object in UCM is always changing and is tangent to the pathway at
each moment.
Drawing a free body diagram for UCM:
Fc always points toward the center of the pathway
ac always points toward the center of the pathway
velocity is perpendicular to Fc & ac and is tangent to the circular pathway.
When object move in circles, they can repeat the same pathway over and over again. One around a
circular pathway is called a revolution.
The circumference (C = 2πr) is the distance an object travels in one revolution.
The period (T) is the time it takes to complete one revolution.
The frequency (f) is how much of a revolution is completed per unit time (T = 1/f) and is measured in
Hertz (Hz).
The velocity can be calculated by dividing the distance (circumference of the circle) by the time
(period). So v = 2πr/T
v= d
t
v = 2πr
T
ac = v2
r
Fc = mac
How do you calculate the speed of an object moving in Uniform Circular Motion??

Velocity (v) (magnitude only = speed)

Acceleration (ac)

Centripetal Force (Fc)
Practice Problems:
1. A 0.5 kg mass is attached to the end of a 1.5 m string. The mass is whirled in a horizontal circle.
The stopper completes each revolution in .5 sec. Find the velocity of the rubber stopper as it moves in
a circle.
2. The Barf-with-Bunning ride at Magic Mountain has a radius of 5 m and spins with a period of 3.1 s.
What is the speed of the occupants of the ride? What acceleration do they experience? What force
does Ben (60 kg) experience as he goes on the ride? (10.1 m/s; 20.4 m/s2; 1224 N)
3. How long does it take for a piece of lettuce to go one time around a salad spinner that has a radius
of 0.20 m that is moving at 15 m/s? What is the centripetal force provider? (.08 sec; FN)
The Centripetial Force is a center pointing force that causes the object to change direction.
Centripetal forces are provided by real forces acting on the object. (FT, Ff, FN, Fg)
(The actual force acting on the object
that causes it to change direction.)
Situation
Centripetal Force Provider
Object on a string or wire
swinging in a circle
Object in a circular drum
or on a circular track
Object going around a curve
Object orbiting another object
What is the centripetal force provider in each situation?
Situation:
Observation: What is pushing or pulling the object?
(What kind of force is causing the object to change direction?)
A ball is tied to a string and twirled in a circle
Tetherball on a pole
A child swings on amusement park swings
A ball rolls around a circular pathway in a wooden hoop
A ball rolls around a vertical circular track (like a roller coaster)
Salad in a salad spinner
Water in a bucket swinging in a circle
object on a tray swinging in a circle
clothes in a washing machine
object on a rotating platform
car going around a curve (exit ramp)
Children playing on a merry-go-round
a satellite orbiting the Earth
the moon orbiting the Earth