Download Uniform Circular Motion (UCM)

Uniform Circular Motion (UCM)
General Physics
Review Questions:

What are Newton’s first two laws of motion?

What would a moving object do if the forces acting on it were balanced?

What does acceleration mean?

What happens to objects when they accelerate?

What causes objects to accelerate?
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, always changing the direction the object is moving.

What kind of REAL FORCES push or pull objects in circular pathways?
The Centripetal 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

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. Provide some examples and diagrams!
Drawing a free body diagram for UCM:
Fc always points toward
ac always points toward
velocity is
Uniform Circular Motion (UCM) (continued)
General Physics
When an object moves in a circle, they can repeat the same pathway over and over again. We say
that it is uniform if….
Once around a circular pathway is called a revolution.
The circumference (C = 2πr)
The period (T)

How do you find the speed/velocity of an object?
How do you calculate the speed of an object moving in Uniform Circular Motion??

Velocity (v) (magnitude only = speed)

Acceleration (ac)

Centripetal Force (Fc)
Example Problem: A red buggy moves in a circle on the front desk.
How fast is it moving?
What is the centripetal acceleration of the buggy?
Equations in this unit….
v= d
t
v = 2πr
T
ac = v2
r
Fc = mac
Fc = m v2
r
Practice Problems: For each problem, draw a diagram of the object moving in a circle. Draw in
arrows to show the direction of the centripetal force, the centripetal acceleration and the
velocity. Make a table of variables identifying the giving quantities and the units. Writhe the
equation, substitute values into the equation and record the answer with the correct units.
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 0.5 sec. Find the velocity of the rubber stopper as it
moves in a circle. What kind of force causes the mass to move 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? What kind of force causes the
occupants to move in a circle? (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)
Uniform Circular Motion Class Work/Homework Problems
Draw a diagram of the object in each situation. Include arrows that represent the direction of the
centripetal force (FC) the centripetal acceleration (ac) and the velocity (v).
1. A .025 kg ball on a 0.5 m string completes a revolution in 0.4 seconds.
a. How far does the ball go in one revolution (circumference of the circle)?
b. What is the speed of the ball?
c. Find the centripetal acceleration of the ball.
d. Find the FT acting on the ball.
2. A 40 kg child sitting 1.1 m from the center of a merry -go-round moves in a circle at a constant
speed of 1.25 m/s.
a. Calculate the centripetal acceleration acting on the child.
b. What kind of force is the centripetal force provider?
c. Find the force of friction exerted on the child.
3.
A .7 kg toy car drives through a portion of a horizontal, circular track. It moves through one half
of a circle with a radius of 2 meters in 3 seconds.
a. What actual force allows the car to travel in a circular path?
Find: b. the distance the car traveled around the curve (half the circumference of the circle)
c. the linear velocity (speed) of the car
d. ac of the car
e. Fc on the car
4. The moon's nearly circular orbit about the Earth has a radius about 3.84 x 108 m. What kind of
force keeps the moon in orbit? If the moon slowed down or stopped moving, what would happen?
Reference Table: Uniform Circular Motion
C = 2πr
v = d/t so… in a circle v = C/T
aC = v2/r
FC = m aC
FC = m v2/r
Fg = mg
aC = centripetal acceleration
C = circumference
F = force
FC = centripetal force
Ff = force of friction
Fg = force of gravity or weight
FN = normal force
Fnet = net force (unbalanced force)
FTen = force of tension
g = acceleration due to gravity (9.8 m/s2 on Earth)
m = mass
r = radius
t = time
T = period
v = velocity
Driving on Curved Roadways
UCM
Conceptual Physics
1. What kind of force keeps a car moving in a curved pathway? What kinds of factors affect the size
of that force?
2. What direction does the force act?
3. Calculate the Fc required to keep a 1000 kg car moving at 10 m/s on a curved road with a radius of
30 m. (show all your work)
4. What would happen if the friction between the road and the car tires was less than that size force?
(Fc calculate in #3)
5. Calculate the size of the force required for the same car to go around the same curve at 15 m/s.
6. What happens to the size of the Fc needed to keep the car moving in a curve as the car goes
faster? What happens to the size of the force of friction as the car goes faster?
7. Why is it important to pay attention to signs like these posted before curved roadways?