Download Circular Motion

Circular Motion
Angular Acceleration
Distance around a Circle

2 r or  d
Circumference

Distance around a circle
r
Period and Frequency



The period is the time it takes an object in uniform
circular motion to complete one revolution of the
circle.
The frequency is how many revolutions an object
in uniform circular motion completes in one period.
Relationship between period and frequency:


T=1/f
F=1/T (unit are hertz, Hz, which is 1/second)
W.S. Ratios cmtp #7
Speed, Velocity, Angular Velocity

Omega*r = ωr
2
 = angular velocity =
 2 f
T
 2 
v = velocity = 
 r = r
 T 
2
v
2
ac = centripetal acceleration =
or  r
r
Centripetal Acceleration

Centripetal Acceleration


Acceleration due to the centripetal
acceleration
If an object is moving in a circular
motion, it is experiencing centripetal
acceleration relative to the plane of
circular motion.
m
ac 
Fc
v2
ac 
r
ac =  2 r
Centripetal Force

Fc  mac
A way to describe what a force is “doing.”
Normal force, gravity, tension − each of these
forces can be a centripetal force if it is
causing an object to move in uniform circular
motion.
Centripetal Acceleration vs.
Acceleration of Gravity

G-force, how many g’s


Vacuum at 600rpm, r = 10cm


Multiple of gravity,
Find T in seconds or f in Hz
Centrifuge at 2000rpm, r = 15cm

Find T in seconds or f in Hz
Relative Motion

Velocity of A relative to B
VA/ B

Velocity of B relative to C
VB / C

Velocity of A relative to C
VA/ C  VA/ B  VB /C

Must add Velocity of A (relative
to B) and Velocity of B (relative
to C) together.
Vector Math






a) Draw a picture showing the way the two
vectors add together
b) Break any vectors at angles into x and y
components
c) Add the x components to find the total
displacement component along that axis
d) Add the y components to find the total
displacement component along that axis
e) Add the total x and y components to find the
total displacement
Show work for each step.
Planet
Avg
Radius
Period (T)
Angular
acceleration
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
57.9
0.241
39.4
150
1
5.92
778
11.9
0.217
5890
248
0.0038
Centripetal
acceleration vs.
mean radius
Centripetal
acceleration vs.
mean radius
Centripetal Force
Q: No force is required for an object to
move in uniform circular motion. After all,
its speed is constant.
 A: Speed is constant, but its velocity is
changing due to its change in direction, which
means it is accelerating. By Newton’s second
law, this means there must be a net force
causing this acceleration.

Summary

Uniform circular motion is movement in a
circle at a constant speed. But while
speed is constant in this type of motion,
velocity is not. Since instantaneous
velocity in uniform circular motion is
always tangent to the circle, its direction
changes as the object's position changes.
Summary
The period is the time it takes an object in
uniform circular motion to complete one
revolution of the circle.
 The frequency is how many revolutions
an object in uniform circular motion
completes in one period.
 T=1/f
 F=1/T

Summary

Since the velocity of an object moving in
uniform circular motion changes, it is
accelerating. The acceleration due to its
change in direction is called centripetal
acceleration. For uniform circular motion,
the acceleration vector has a constant
magnitude and always points toward the
center of the circle.
Summary

Newton's second law can be applied to an
object in uniform circular motion. The net
force causing centripetal acceleration is
called a centripetal force. Like centripetal
acceleration, it is directed toward the
center of the circle.
Summary

A centripetal force is not a new type of force;
rather, it describes a role that is played by one
or more forces in the situation, since there must
be some force that is changing the velocity of
the object. For example, the force of gravity
keeps the Moon in a roughly circular orbit
around the Earth, while the normal force of the
road and the force of friction combine to keep a
car in circular motion around a banked curve.
Homework

Chapter 6

Projectile Motion

# 4, 5, 6, 10

# 32, 34, 35, 36, 45, 61, 63, 64,65

When calculating time an object is in the air, consider
the final height or displacement in the y direction.
That is, how high is it when it is laying on the ground.