Chapter 8 Rotary Motion
DEMOS:
rotation of rods
disk acceleration (varying mass location)
bike wheel (
Launch lab P197
how do different objects rotate as they roll?
8:1 Describing Rotary Motion



Rotation
o to describe the motion of an object we must know
position and velocity at any instant in time.
o but different points on a rotating objects will have
different speeds.
o prefer fewer numbers to keep track of.
Let's say we have a rigid wheel that will not deform under rotation
o if we rotate the wheel,
 points closer to the center will move through a smaller linear
distance
 points farther from the center will move through a larger linear
distance
 but all points on the wheel will move through the same angular
distance.
o define this angular distance, 
 measuring 
  = s/r
 s - length of arc (linear distance)
 r - radius of circle
  - angle measured in radians.
 2 radians = one complete circle = 360o
How quickly did the angular position change?
o Define average angular velocity

o
Instantaneous angular velocity


Is the angular velocity changing?
o Define average angular acceleration

o
Instantaneous angular acceleration

Summary of angular and linear measurements:
Quantity
Linear
Angular
Displacement
d (m)
Θ (Rad)
velocity
v (m/s)
ώ (rad/s)
2
acceleration
a (m/s )
α(rad/s2)
Relationship
D=r Θ
V=rώ
A=r α
Assignment:
Practice problems p200 #1-4
Section 8-1 review p200
8:2 Rotational Dynamics

Torque
o
o
o
Consider a door that is closed. You want to open the door
which means causing a change in its rotational motion.
What will cause the largest possible change in the rotational
motion?
 as large a force as possible
 applied at the correct point
 and in the correct direction
Look at the door from above
 F - Force vector
o

r - displacement vector from axis of rotation to point of application
of force.

 - angle between force and displacement vector

d - the perpendicular distance from the center of rotation to the line
of action of the force.
Torque  (tau) is defined as the vector product of r and F
 torque is a vector and has units of N-m
 convention
 CCW rotation: torque > 0
 CW rotation: torque < 0
EQUATION:
τ =r×F
Assignment:
Practice problems p 203 #11-15
Practice problems P205#16-20
Torque WS
TORQUE LAB
●MOMENT OF INERTIA
(resistance to change in rotation of an object)
EQUATION:
2
I = mr
I= moment of inertia
M=mass
r=distance from the axis of rotation
NEWTON’S SECOND LAW FOR ROTARY MOTION

 net
I
ASSIGNMENTS:
Practice problems p208 #21-24
Rotary motion WS
Practice problems p210 #25-29
8.3 EQUILIBRIUM
Center of Mass: is the pt on the object that moves in the same way that a point particle
would move.
Locating the center of mass:
UNIFORM OBJECT: where it balances
Center of mass and stability
Conditions for equilibrium
PRECESSION EXPLANATION
Precession of Spinning Wheel
A spinning wheel which is held up by one end of its axle will
precess in the sense shown if it has that direction of spin. If
the spin is reversed, it will precess in the opposite direction.
The sense of precession is determined by the direction of the
torque due to the weight of the spinning wheel. That torque is
perpendicular to the angular momentum of the wheel.
Precession, Top View
The spin angular momentum is along the rotation axis as shown, but the torque about the
support point is in a direction perpendicular to the angular momentum. The torque
produces a change in L which is perpendicular to L. Such a change causes a change in
direction of L as shown but not a change in its size. This circular motion is called
precession.
Precession Torque
The spin angular momentum is along the rotation axis as shown, but the torque about the
support point is in a direction perpendicular to the angular momentum. The torque
produces a change in L which is perpendicular to L. Such a change causes a change in
direction of L as shown but not a change in its size. This circular motion is called
precession.
If the wheel is not spinning, the apparatus just rotates downward toward a vertical
orientation. If you curl the fingers of your right hand in the direction of that expected
rotation, then your thumb will point perpendicular to the spin axis in the direction of the
torque produced by gravity. The tip of the angular momentum vector, and therefore the
axle of the wheel, will precess in that direction.
REVIEW
Rotational-Linear Parallels