Transcript Rotational Motion - Physics & Astronomy | SFASU

Chapter 8
Rotational Motion
Rotational Motion
Angular Distance (q)
o Replaces distance for rotational motion
o Measured in

Degrees

Radians

Revolutions
q
Radian Measure
r
r
1 rad
r
1 rad = 57.3 degrees
2p rad in one circle
Windows Calculator
Rotational Motion
Speed of Rotation (w)
 w = Angle covered/Time required
o
o
= Dq/Dt
Note similarity to v = Dx/Dt
o Measured in



degrees/second
radians/second
revolutions/second
w
Rotational Motion
Angular Acceleration - Measures how
angular velocity is changing (a)
 a = Dw/Dt Note similarity to a = Dv/Dt
o Measured in …



degrees/s2
radians/s2
revolutions/s2
Rotational Inertia

Property of an object that resists
changes in rotation
• For linear motion mass was a measure of
inertia
• For rotational motion Moment of Inertia (I)
is the measure of rotational Inertia
Moments of Inertia
Depends on …
o Mass of the Object
o Axis of Rotation
o Distribution of Mass in the Object
Moments of Inertia
Standard Shapes
Moment of Inertia
Inertia Bars
Ring and Disk on Incline
Metronome
People walking
Weighted Stick - Bare Stick
Torque
Product of Force and Lever Arm
o Torque = Force X Lever Arm
Examples:
o Balance
o See-Saw
o Wrench
W1d1 = W2d2
Sample Torque Problem
(0.5 kg)(9.8 m/s2)(0.1 m) = (0.2 kg)(9.8 m/s2)d
0.5 kg
d
(0.1 m)
0.2 kg
d  0.25 m
F
Line of
Action
Lever
Arm
Torque Examples
Torque
Just as unbalanced forces produce
acceleration, unbalanced torques
produce angular acceleration.
Compare:
SF = ma
St = Ia
Center of Mass
Average position of the mass of an
object
o Newton showed that all of the mass of the
object acts as if it is located here.
o Find cm of Texas/USA
Finding the Center of Mass
Line of action
Pivot point
Lever arm
Torque
weight
No
Torque
High Jumper
Stability
In order to balance forces and torques,
the center of mass must always be
along the vertical line through the base
of support.
Demo
• Coke bottle
• Chair pick-up
Stability
Base of Support
Stability
Which object is most stable?
Centripetal Force
Any force that causes an object to
move in a circle.
Examples:
•
•
•
•
•
Carousel
Water in a bucket
Moon and Earth
Coin and hanger
Spin cycle
Centripetal force
F = mac
= mv2/r
2
= mrw
Centrifugal force
Fictitious center fleeing force
o Felt by object in an accelerated reference
frame
Examples:
o Car on a circular path
o Can on a string
Space Habitat
(simulated gravity)
w
r
Space Habitat
(simulated gravity)


“Down” is away from the center
The amount of “gravity” depends on
how far from the center you are.
Angular Momentum
L = (rotational inertia) X (angular velocity)
L = Iw
Compare to linear momentum:
p = mv
Linear Momentum and Force
Angular Momentum and Torque
Linear
o Impulse
Rotational
o Rotational Impulse
SF = Dp/Dt
Dp = SF Dt
St = DL/ Dt
DL = St Dt
Conservation of Momentum
Linear
o If SF = 0, then p is constant.
Angular
o If St = 0, then L is constant.
Conservation of
Angular Momentum
Ice Skater
Throwing a football
Rifling
Helicopters
Precession
Rifling
Football Physics
L
Helicopter Physics
Rotation of Rotor
Body Rotation
Tail rotor used to produce
thrust in opposite direction
of body rotation
Precession
Age of Aquarius
Linear - Rotational Connections
Linear
x (m)
Rotational
q (rad)
v (m/s)
w (rad/s)
a (m/s2)
a (rad/s2)
m (kg)
F (N)
I (kg·m2)
t (N·m)
p (N·s)
L (N·m·s)