Rotation, angular motion &
angular momentom
Physics 100
Chapt 6
Rotation
Rotation
d1
d2
The ants moved different
distances: d1 is less than d2
Rotation
q
q1
q2
Both ants moved the
Same angle: q1 = q2 (=q)
Angle is a simpler quantity than distance
for describing rotational motion
Angular vs “linear” quantities
Linear quantity
distance
velocity
=
change in d
elapsed time
symb.
d
v
Angular quantity
symb.
angle
angular vel.
change in q
= elapsed
time
q
w
Angular vs “linear” quantities
Linear quantity
distance
velocity
acceleration
=
change in v
elapsed time
symb.
d
v
a
Angular quantity
symb.
angle
q
angular vel. w
angular accel. a
change in w
= elapsed
time
Angular vs “linear” quantities
Linear quantity
symb.
distance
velocity
acceleration
mass
d
v
a
m
resistance to change in the
state of (linear) motion
moment
arm
x
Angular quantity
symb.
angle
q
angular vel. w
angular accel. a
Moment of Inertia
I (= mr2)
resistance to change in the
state of angular motion
M
Moment of inertia
= mass x (moment-arm)2
Moment of inertial
M
M
x
I  Mr2
r
I=small
r
r = dist from axis of rotation
I=large
(same M)
easy to turn
harder to turn
Moment of inertia
Angular vs “linear” quantities
Linear quantity
distance
velocity
acceleration
mass
Force
symb.
Angular quantity
symb.
d
angle
q
v
angular vel. w
a
angular accel. a
m
moment of inertia I
F (=ma)
torque
t (=I a)
Sameforce;
force;
Same
bigger
torque
even
bigger
torque
torque = force x moment-arm
Teeter-Totter
His weight
produces a
larger torque
F
Forces are
the same..
but Boy’s moment-arm is larger..
F
Angular vs “linear” quantities
Linear quantity
symb.
distance
velocity
acceleration
mass
Force
momentum
d
v
a
m
F (=ma)
p (=mv)
Angular momentum
is conserved: L=const
Angular quantity
angle
symb.
q
angular vel. w
angular accel. a
moment of inertia I
torque
t (=I a)
angular mom. L (=I w)
Iw = Iw
Conservation of angular
momentum
w
I
Iw
Iw
High Diver
Iw
w
I
Iw
Conservation of angular
momentum
Iw
w
I
Angular momentum is a vector
Right-hand
rule
Conservation of angular
momentum
L has no vertical
component
No torques possible
Around vertical axis
vertical component of L= const
Girl spins:
net vertical
component of L
still = 0
Turning bicycle
L
These compensate
Torque is also a vector
example:
pivot
point
another
right-hand rule
F
t is out of
the screen
Thumb in
t direction
F
wrist by
pivot point
Fingers in
F direction
Spinning wheel
t
F
wheel precesses
away from viewer
Angular vs “linear” quantities
Linear quantity
symb.
distance
velocity
acceleration
mass
d
v
a
m
Force
momentum
F (=ma)
p (=mv)
kinetic energy
½ mv2
I
w
V
Angular quantity
angle
symb.
q
angular vel. w
angular accel. a
moment of inertia I
torque
t (=I a)
angular mom. L (=I w)
rotational k.e. ½ I w2
KEtot = ½ mV2 + ½ Iw2
Hoop disk sphere race
Hoop disk sphere race
I
I
I
Hoop disk sphere race
KE = ½ mv2 + ½
Iw
2
KE = ½ mv2 + ½ Iw2
KE = ½ mv2 + ½ Iw2
Hoop disk sphere race
Every sphere beats every disk
& every disk beats every hoop