Chapter 9: Rotational Motion
Rigid body instead of a particle
Rotational motion about a fixed axis
Rolling motion (without slipping)
Rotational Motion
Concepts of rotational motion
Angular Quantities
Kinematical variables to describe the rotational motion:
Angular position, velocity and acceleration
l

( rad )
R
 d
  lim

t 0 t
 dt
( rad/s )
ave
 d
  lim

t 0 t
 dt
2
( rad/s )
 ave
Rotational Motion
Angular Quantities: Vector
Kinematical variables to describe the rotational motion:
Angular position, velocity and acceleration
z
Vector natures
l

( rad )
R
 ˆ d  ˆ
ˆ
 k  lim t  0
k
k ( rad/s )
t
dt
 ˆ d  ˆ
ˆ
 k  lim t  0
k
k ( rad/s 2 )
t
dt
x
Rotational Motion
R.-H. Rule
y
“R” from the Axis (O)
Solid Disk
Solid Cylinder
Rotational Motion
Kinematical Equations for constant
angular acceleration
Conversion : x   , v   , a  
1 2
(1)    0   0t  t
2
(2)    0  t
(3)     2 ( -  0 )
2
2
0
Note :   constant
Rotational Motion
Rotational Motion
College Physics: Motion along a Straight Line
On a merry-go-round, you decide to put your toddler on an
animal that will have a small angular velocity. Which
animal do you pick?
A. Any animal; they all have the same angular velocity
B. One close to the hub
C. One close to the rim
vtan= same = r11= r22
Tooth spacing is the same
2
=
1
2r1 2r2
=
N1
N2
N1
N2
Rotational Motion
3
w=10 rad/s
=0.8 x50=40 m/s
=10^2x0.8=80m/s
Rotational Motion
Rotational Motion
Finding the moment of inertia for common shapes
Rotational Motion
Rotational Motion
9-36
Rotational Motion
Rotational Motion
Rotational Motion
Conservation of energy in a well
Find the speed v of the bucket and the angular velocity w of the cylinder just as the bucket
hits the water
+0
Rotational Motion
Rotational Motion
Relationship between Linear and Angular
Quantities
 l
(1)      t (like l  v t )
 R
 l  ( R )t
 v  R
dv
d
(2) a tan 
R
dt
dt
 a tan  R
(3) a rad
v 2 (R)2
2


 R
R
R
Rotational Motion
atan
arad