# Lecture 37

```Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 37
Hw: Chapter 15 problems and exercises
Orbital motion
Conservation of Angular Momentum
Moment of Inertia
For symmetrical objects rotating about their axis of
symmetry:

2
L  I (rhr ); I   mi ri
i
A block of mass M is cemented to a circular platform
at a distance b from its center. The platform can
rotate, without friction, about a vertical axle through
its center with a moment of inertia, Ip. If a bullet of
mass m, moving horizontally with velocity of
magnitude vB as shown, strikes and imbeds itself in
the block, find the angular velocity of the platform
after the collision.
b
vB
axle
top view
L before = L after
I aa  I bb
L = I wheelw0
I wheelw0 = -I wheelw0 + (I man + I platform )wnew
What is the moment of inertia of a disk of
axis through its center?
Rotational Kinetic Energy
1
2
2
KE  m(Vr  V )
2
1 2
KE  I
2
1 2
1
2
KE  mv cm  I cm
2
2
E top = PE top
F
R
O
E bottom = KE bottom
PE top = KE bottom
V
w=
R
KE bottom
mV
I0w
=
+
2
2
KE bottom
2
&aelig;
&ouml;
I0 V
= &ccedil;m + 2 &divide;
&egrave;
R &oslash; 2
2
2
Have a great day!
Hw: Chapter 15 problems and
exercises
```