Angular Momentum in Collisions
Test #2
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General motion of a rigid body
Collisions involving rotation
Frequency
6
4
2
25
23
21
19
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13
11
7
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5
1
3
0
Text Section 11.6
Average=12.2
Stdev= 4.7
Physics 1D03 - Lecture 26
Angular momentum of a particle:
of a rotating rigid body:
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Physics 1D03 - Lecture 26
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Quick Quiz 44
L = r × p = r × ( mv )
L=Iω
A block is sliding along a surface, following a straight
line, and not rotating about its centre of mass. The
angular momentum vector of the block:
In general, for a moving, rotating rigid body,
L = r × ( mv CM ) + I CM ω
a) points out of the surface
b) lies in the surface, but perpendicular to the motion
c) is zero – the block is sliding in a straight line
The first term is called the “orbital” angular momentum
and the second term is the “spin” angular momentum.
Physics 1D03 - Lecture 26
d) not enough information
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Quick Quiz 45
Collisions: Collisions can conserve angular momentum
as well as linear momentum.
A student sits on a tree branch overhanging a merrygo-round platform that rotates freely.
Total linear momentum is conserved if there is no external
r
force during the collision.
r
Fexternal =
I.
dp
dt
a) increases
b) decreases
c) stays the same
Total angular momentum is conserved if there is no external
torque during the collision.
r
r
τ external =
dL
dt
II. He then jumps straight up and hangs onto the tree branch.
Angular momentum may be calculated about any axis. Usually
it is convenient to use an axis through the centre of mass,
unless one of the colliding objects actually rotates about
some other fixed axis.
Physics 1D03 - Lecture 26
First, he jumps straight down and lands on the platform.
The angular velocity of the platform:
The angular velocity of the platform:
a) increases
b) decreases
c) stays the same
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Rotating
Rotatingrods
rodsdropped
droppedon
onbearing
bearingdemo
demo
Quick Quiz 46
A metre stick (mass M, length L= 1m) is suspended
from one end by a frictionless pivot at P. A ball of
mass m, velocity v0, strikes the other end of the
(stationary) stick at right angles, and stops (final
velocity of the ball is zero).
The metre stick is resting on a frictionless
surface (not attached to anything ) before the
ball hits the end at right angles. Assuming the ball
still stops, what should we write for the stick?
P
Now there is no external force. So,
Which of the following describe the motion of the stick
after the collision? (Answer True, False, or Maybe for
each one.)
Linear momentum is conserved:
M vCM = m v0
CM
Angular momentum is conserved:
ICM ω = mv0 L/2
A) ICM ω = mv0L/2
B) IP ω = mv0L
C) MvCM = mv0
D) ½ mv02 = ½ IP ω 2
If the collision is elastic (it may not be),
kinetic energy is conserved:
v0
Physics 1D03 - Lecture 26
v0
½ mv02 = ½ IP ω2 + ½ M v2CM
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2
Example 25
Quick Quiz 47
A stick (uniform thin rod) is lying on the ice. A
hockey puck hits the stick, at right angles, and
the stick starts to slide. Point P is on the end
farthest from where the puck hits.
Where (on the bat) should a baseball player hit the ball so that
the bat doesn’t hurt his hands?
P
Immediately after the collision, the end P will
start to move:
An equivalent, simpler problem: Suppose the bat
is a stick, and we hold it at the end (point P).
Where should we hit the stick with a ball so that
it will (momentarily) rotate about point P after
the collision, without any external force applied
at P ?
CM
A) in a direction parallel to v0
B) in a direction opposite to v0
C) It depends where the puck hits
P
r
The ball applies a brief impulse F∆t = −∆pball
to the stick.
v0
Physics 1D03 - Lecture 26
CM
F∆t
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Real
Realbat
batsuspended
suspended
Summary
In general, for a rigid body,
L = r × ( mv CM ) + I CM ω
In collisions, angular momentum will be conserved if
there is no external torque.
Physics 1D03 - Lecture 26
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