Rotational Motion Chapter 9: Rotational Motion Rigid body instead of a particle Rotational motion about a fixed axis Rolling motion (without slipping)
Rotational Motion Chapter 9: Rotational Motion Rigid body instead of a particle Rotational motion about a fixed axis Rolling motion (without slipping)
Dec 17, 2015
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Rotational Motion
Chapter 9: Rotational Motion
Rigid body instead of a particleRotational motion about a fixed axisRolling motion (without slipping)
Concepts of rotational motion
Rotational Motion
Angular QuantitiesKinematical variables to describe the rotational motion:Angular position, velocity and acceleration
)(
)(
)(
2
0 t
0 t
rad/s dt
d
t lim
rad/s dt
d
t lim
rad R
l
ave
ave
Rotational Motion
Angular Quantities: VectorKinematical variables to describe the rotational motion:Angular position, velocity and accelerationVector natures
x
y
z
R.-H. Rule
)(
)(
)(
2rad/s k dt
dkk
rad/s k dt
dkk
rad R
l
ˆˆlimˆ
ˆˆlimˆ
0
0
t
t
t
t
Rotational Motion
“R” from the Axis (O)
Solid Disk Solid Cylinder
Rotational Motion
Kinematical Equations for constant angular acceleration
constantNote
ax Conversion
:
)(
:
020
2
0
200
-2 (3)
(2)2
1 (1)
, ,
t
t t
v
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 velocityB. One close to the hubC. One close to the rim
Rotational Motion
vtan= same = r11= r22
Tooth spacing is the same 2r1 N1
2r2 N2
=
2
1= N2
N1
Rotational Motion
=0.8 x50=40 m/s
=10^2x0.8=80m/s
w=10 rad/s3
Rotational Motion
Finding the moment of inertia for common shapes
Rotational Motion
Rotational Motion
Rotational Motion
9-36
Rotational Motion
Rotational Motion
Rotational Motion
Conservation of energy in a well
+0
Find the speed v of the bucket and the angular velocity w of the cylinder just as the bucket hits the water
Rotational Motion
Rotational Motion
Relationship between Linear and Angular Quantities
RR
R
Ra
Ra
Ra
R
Rl
l R
l
222
rad
tan
tan
( (3)
(2)
)(
(1)
)
d
d
d
d
v
v
v
v
tt
t
t like t )(
atan
arad
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