Download Lectures 39, 40, 41, 42

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 39, 40,
41, 42
Hw: Chapter 15 problems and exercises
Gyroscopic precession
• The precession of
a gyroscope
shows up in many
“common”
situations.
A rotating flywheel
Ch. 17 Statics


Fext  0  ext  0
Ch. 17 Statics
Parallel-Axis Theorem
I p = I cm + Md
2
A rigid body has a lower moment of inertia about
an axis through its center of mass than about any
other parallel axis
I cm = I p - Md
2
There is a ladder against a wall. There is no
friction at the wall and the coefficient of
friction at the floor is . At what angle can the
ladder be placed so that it would slip if the
angle were decreased infinitesimally?
Simple harmonic oscillator
Examples
Lots of stuff Vibrates or Oscillates:
–Radio Waves
–Guitar Strings
–Atoms
–Clocks, etc…
Why do we care?
Lots of engineering problems are
oscillation problems
– Buildings vibrating in the wind
– Motors vibrating when running
– Solids vibrating when struck
– Earthquakes
Resonance
The forces
No force
Force in –x
direction
Force in +x
direction
More Detail
Time
Some Terms
Amplitude: Max distance
Period: Time it takes to get
back to here
A block with mass m is attached to
the end of a spring, with spring
constant k. The spring is stretched
a distance L and let go at t=0
• Find the position of the mass at all
times
• Where does the maximum speed
occur?
• What is the maximum speed?
If the block is pulled a distance x1 to the right
and released from rest, how long will it take the
block to return to its equilibrium position?
How does this time change if the displacement
is increased from x1 to 2x1?
How fast will the block be moving at its
equilibrium position for the x1 displacement?
Average 87
Median 90
60
54
50
40
28
30
20
10
4
10
3
3
2
0
1
2
3
4
5
>90 >80 >70 >60 >50
6
>40
7
8
>20
9
A bullet of mass m is fired with velocity of magnitude Vm
into a block of mass M. The block is connected to a
spring constant k and rests on a frictionless surface.
Find the velocity of the block as a function of time.
(Assume the bullet comes to rest infinitely quickly in
the block, i.e. during the collision the spring doesn’t
get compressed.)
Vm

Simple pendulum
How long does it take to return to the equilibrium?
Resonance
F0 cos Dt
amplitude
d 2x
dx
m 2  b  kx  F0 cos  D t
dt
dt
F0
m
x(t ) 
cos( D t   )
2
2 2
b
D
k

2
  D   2
m
m

D
Have a great day!