Download Circular Motion Notes

Circular Motion Notes
Uniform circular motion is the motion of
an object in a circle at a constant speed.
• As an object moves in a
circle, it is constantly changing
its direction.
• In all instances, the object is
moving tangent to the circle.
* constantly accelerating
Δ
a = v
t
d
Δ
v = Δ
so
t
a change in direction OR a change in speed will result in
acceleration
and
Circular Motion Notes
Rotation: object
is turning around
an internal axis
Revolution: object is
moving around an
external axis
Finding Radians:
As a general rule, when doing these calculations you should NOT leave any answers in
terms of π!
(Multiply it out!)
A full circle has exactly 2π radians.
To calculate radians, multiply the degrees by π/180.
(Example: 120° = 2π/3 radians)
Circular Motion Notes
150 degrees = ____________ radians?
150 degrees x π
180
=
2.62 radians = 2.62 rad
3.14 ≠ π
π
You are expected to use the (pi) button
on your calculator for all of these problems!
1 revolution = 1 full turn of the circle
1) 310° = ? radians
2) 7 radians = ? degrees
3) A bicycle tire travels 4.5 revolutions.
a) How many radians is this?
b) How many degrees did it roll?
Circular Motion Notes
Linear (tangential) Velocity
In one full rotation, the wheel has turned th e distance
of the circumference.
Position on the circular path will determine
the linear velocity of an object.
Linear velocity is calculated by multiplying the angular
velocity by the radius:
v = ω x radius
B
A
Two objects A and B are located on a spinning disk. Object A sits at a radius of 2 meters from the center, while object B sits 4 meters from the center. If the angular speed for the disk (ω ) is 200 rad/s, what are the linear speeds for objects A and B, respectively?
Circular Motion Notes
Angular vs. Linear Velocity
Linear velocity = tangential velocity
Every point on a rotating body has the same
angular velocity even though every point does
not have the same linear velocity.
This is what makes angular velocity a useful
measure of the rate of rotation.
The blade of a lawn mower is rotating at an angular speed of 17 rev/s. The tangential speed of the outer edge of the blade is 32 m/s. What is the radius of the blade?
Circular Motion Notes
Centripetal Motion
The word "centripetal" means "center- seeking."
Since the acceleration for circular motion points
toward the center of the circle, we call it
centripetal acceleration.
The force for circular motion is called centripetal
force since it is toward the center of the circle.
Centripetal Force
The mass of the object
times the square of its
velocity, divided by the
radius of the orbit or
rotation.
The force toward the center may be caused
by gravity, friction, or another force.
Circular Motion Notes
Centripetal force holds an object in a circular path. Three properties govern the amount of centripetal force on an object:
1. The smaller the mass, the smaller the centripetal force needed.
Fc
Fc
2. The smaller the velocity of the object, the less centripetal force needed. v
v
Fc
Smaller Fc needed to force the object into orbit.
Fc
Larger Fc is needed to counteract the greater velocity (v).
Circular Motion Notes
3. The smaller the radius of the path, the more centripetal force you will have to apply. Fc
Fc
More force is needed here
Less force is needed
A 45 kg child riding a Ferris wheel has a tangential speed of 8.5 m/s. Find the magnitude of the centripetal force on the child if the distance from the child to the axis of the wheel is 18 m.
Circular Motion Notes
Circular Motion
The blue object is moving with uniform circular motion around the red center. The object has a velocity that is tangent to the circular path.
The object has an acceleration toward the center, called centripetal acceleration.
Centripetal Acceleration
ac = v2
r
Centripetal acceleration accelerates the object toward the center of the circular path
ac = centripetal acceleration (m/s 2)
v = velocity (m/s)
r = radius of the circle (m)
Attachments
UniformCircularMotion.gif