17
8.22
From section 8.7 (see Figure 8.7.1), the instantaneous center of rotation is the
point
.
If
O
x
is the distance from the center of mass to
O
and
2
l
is the distance from
the center of mass to the center of percussion
O
′
, then from eqn. 8.7.10 …
22
1
21
2
cm
I
lM
l
x
MM
==
=
1
2
l
6
l
x
=
8.23
In order that no reaction occurs between the table surface and the ball, the ball
must approach and recede from its collision with the cushion by rolling without slipping.
Using a prime to denote velocity and rotational velocity after the collision:
ˆ
cm
cm
P
vv
m
′
=−
()
ˆ
cm
cm
P
ha
I
ωω
′
=
−−
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
 Center Of Mass, Mass, Work

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