Circular Motion

Angular Acceleration

Distance around a Circle

Circumference Distance around a circle

r

2 or r d

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)

Speed, Velocity, Angular Velocity

Omega*r = ωr

22

2 = angular velocity = 2

2 = velocity = =

= centripetal acceleration = or c

fT

v r rT

va r

r

W.S. Ratios cmtp #7

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.

2

2

=

cc

c

c

ma

F

va

r

a r

Centripetal Force

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.  

c cF ma

Centripetal Acceleration vs. Acceleration of Gravity

G-force, how many g’sMultiple of gravity,

Vacuum at 600rpm, r = 10cmFind T in seconds or f in Hz

Centrifuge at 2000rpm, r = 15cmFind T in seconds or f in Hz

Relative Motion

Velocity of A relative to B

Velocity of B relative to C

Velocity of A relative to C Must add Velocity of A (relative

to B) and Velocity of B (relative to C) together.

/A BV

/B CV

/ / /A C A B B CV V V

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 57.9 0.241 39.4

Venus

Earth 150 1 5.92

Mars

Jupiter 778 11.9 0.217

Saturn

Uranus

Neptune

Pluto 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/fF=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.