Chapter 7: Circular Motion
______________________ – Spin about an axis located within the body
Example:
______________________ – Spin about an axis located outside the body.
Example:
Linear Parameter
Distance
Angular Parameter
Symbol
Name
“theta”
Velocity
“omega”
Acceleration
“alpha”
Time
Time
t
n/a
Units
Sec, min, hours
Angular Quantities compared to linear quantities:
Distance:
Note: This equation for the angular distance only works for radians.
1 revolution = 2 radians = 360o
Example: A point on the edge of a wheel of radius 3.50 m travels 1.75 m as the wheel turns. What is
the angular distance the point travels?
How far has this point traveled in degrees?
How many revolutions has this point gone through?
Angular Velocity (
): The speed at which the object is going around in a circle. Velocity depends
on the direction. Direction in this case is either clockwise or counter clockwise.
Units: rev./s or rad/s. However, your final answer should always be in rad/s
Angular Acceleration: When an object is traveling in a circle faster and faster or slower and slower.
The object is changing the rate of its spin.
Units: rad/s2
Linear Equations compared to Angular equations:
Linear
Angular
v = vo + at
d = vot + ½ at2
v2 = vo2 + 2ad
d = ½(vo + v)t
Example: A Bicycle wheel begins rotating from rest. After _______ it has an angular velocity of
100 rad/s. What is its angular acceleration?
Example: A dentist’s drill starts from rest. After 3.2 sec of constant angular acceleration it turns
at a rate of 2.51x104 rev/min. Determine the angle (in radians) through which the drill rotates
during this period.
Example: A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits near the
axis of rotation. The merry-go-round makes a complete revolution every second. The gentleman
bug’s angular velocity is…
1. Half the ladybug’s
2. The same as the ladybug’s
3. Twice the ladybug’s
4. Impossible to determine.
Example; When a wheel of radius R rotates about a fixed axis as in the figure below, which of the
following statements are ________?
a. All points on the wheel have the same angular speed.
b. All points on the wheel have the same tangential velocity
c. All points on the wheel have the same angular acceleration
Centripetal Acceleration and Centripetal Force:
Example: Explain why it feels like you are pulled to the right side of the car when going around a
left-handed turn?

Angular acceleration (
) arises when a spinning object is speeding up or slowing down its
spin. (Example: A car tire as a car is speeding up)

________________ acceleration (
) has to do with the fact that the _______________
of an object is always changing even if the speed of the spin is not. (Example: Earth’s orbit
around the sun)

An object moving in circular motion is inherently accelerating (centripetal acceleration) because
it is constantly changing direction. It must therefore have a net force continually acting on it.
We call this net force the ____________________.

The centripetal force (which is the new force which causes circular motion) always points
toward __________________________________.
Example: A car rounds a curve while maintaining a constant speed. Is there a net force on the car
as it rounds the curve? Explain.
Equations for Centripetal Acceleration:
If an object is traveling in a ______________ there MUST be a ________________ on that
object causing a ______________________.
One equation for Centripetal Acceleration:
Where v = linear/tangential velocity (given in m/s)
R = radius (in meters)
______________(T): The time it takes for on object to complete one full rotation or revolution.
(Remember: 1 revolution or rotation = 360o = 2 radians)
Another equation for Centripetal acceleration:
Where T is the period or the time it takes for one revolution. (in seconds)
R = Radius of spin (in meters)
Example: A child 1.35 m from the center of a merry-go-round is moving with a period of 2.0
minutes. What is her centripetal acceleration in m/sec 2?
Example: On a day when the roads are icy, the coefficient of friction between a typical tire and the
pavement is 0.200. What is the maximum speed a car can make a turn of radius ________?

Roads can be banked (or tilted), to reduce the need for friction to make a turn.
Example: If a car of mass, m, is going to drive at a linear velocity, v, on a road. At what angle, ,
must the road be banked?

Note: Banking angle does not depend upon ___________.
Example: A girl on a merry-go-round is standing 5 m from the center, and holds a yoyo. If the
string makes an angle of 3o with the vertical, how fast is she going?
Example: A daredevil drives a motorcycle on a loop the loop track. What is the slowest he can go
and still make it? Remember: mg is constant, but the normal force varies with the speed.
If the man and the motorcycle have a combined mass of 350 kg, what is the normal force at the
bottom of the ramp?
Universal Gravity:
Explain why a bowling ball moving at ____ km/s would end up orbiting the Earth.
Law of Universal Gravitation:
Every body in the universe attracts every other body with a mutual force that is directly
proportional to the product of their masses and inversely proportional to the square of the distance
between their centers.
Where G = 6.67x10-
11
N m2/kg2 (The Universal Gravitation Constant)
M1 and M2 = The masses of the two objects in kg
R = the distance between the two objects in meters
Example: He is obviously attracted to her. But, how much force of attraction is there? Assume:
His mass = _____, Her mass = 52 kg, and separated by 0.75 m
Example: A satellite is orbit around the Earth makes one complete revolution every 3.00 days. At
what altitude is the orbit? (Mass of Earth = 6.0 x1024 kg, Radius of Earth = 6.4 x 106 m)
How do the tides work?
What is a spring tide? (picture or explanation)
What is a neap tide? (picture or explanation)