Physics 103
Exam IV
7 December 2011
Name ______________________________ [0 or 1 point]
Part A: Select and circle the best answer for each of the following questions:
[0 or 1 point each]
1.
A pendulum swinging on the Moon would have a frequency _____ one swinging on the Earth.
a) smaller than
b) the same as
c) larger than
d) equal to
2.
The time rate of change in angular velocity is defined to be the
a) angular velocity
b) angular momentum
c) moment of inertia
d) angular acceleration
3.
A simple pendulum on Earth swings at angular frequency of frequency of 5 rad/sec. How
long is the pendulum?
a) don’t know—have to know the mass
b) 2.55 m
c) 1.96 m
d) 0.39 m
4.
The SI units of angular torque are _________________.
a) kg m2/s
b) N m
c) N/m
d) kg m/s2
5.
The angular velocity vector for a spinning rigid body is directed __________, according to the
right-hand-rule.
a) along the rotational axis
b) perpendicular to the rotational axis
Part B: Solve the following problems. Show your work. [0, 1, or 2 points each]
6.
A brake pad exerts a frictional force of 40 N against the edge of a spinning disk. The axis of
rotation is perpendicular to the plane of the disk, through its center. The spinning disk has
mass of M = 15 kg, a radius of R = 0.5 m, and a moment of inertia I = 15.0 kgm2 . What is the
magnitude of the angular acceleration of the disk about its axis of rotation?
1
7.
A compact disk starts from rest and accelerates constantly to an angular speed of 300 rev/min
(31.4 rad/s), taking t = 2.00 seconds to do so. Compute the angular displacement during this
time interval.
8.
A particle of mass m = 2.00 kg has a velocity of v = 4.00
m/sec parallel to the x-axis. What is the angular momentum
of the particle about the origin when its position is at
r = 2.00 m from the origin along a line making a 30o angle
with the x-axis? [Including direction!]
2
9.
An object of unknown mass is attached to an ideal spring with a force constant 100 N/m. The
object vibrates on the spring at a frequency of 5.00 Hz. Evaluate the mass of the object.
10. A hollow sphere begins at rest, at height h,
and rolls without slipping down an inclined
plane. Use energy conservation to find the
speed, v, of the spherical shell at the bottom
of the incline.
2
h  2.0m , R  0.5m , M  10kg , I  MR 2
3
3
Part C: Work the following problem. Show your work, and use words
and phrases to describe your reasoning. [10 points]
11. An ideal string is wrapped around a pulley. Hanging from the free end
of the string is a mass, m = 10.0 kg. The axel of the pulley is
frictionless, but the string does not slip on the pulley.
Calculate a) the acceleration of the mass, m and
b) the tension, T, in the string.
1
M = 4.0 kg and R = 5.0 m and I  MR 2 .
2
Don’t forget the free body diagrams.
4
And, from 2009:
5
Vectors:

A  Ax xˆ  Ay yˆ  Az zˆ

A  A  Ax2  Ay2  Az2

Cx = Ax + Bx
Cy = A y + B y
 
A  B  Ax Bx  Ay B y  Az Bz
 AB cos 
Kinematics:
Constant
acceleration:

1
2

a
aˆ  
a
Cz = Az + Bz
 
A  B  AB sin 

r  xxˆ  yyˆ

 dr
v
 vx xˆ  v y yˆ
dt
direction by right
hand rule

 dv
a
 ax xˆ  a y yˆ
dt
  
r  rf  ri


r
 v 
t


v
 a 
t
Earth’s gravity: g = 9.8 m/sec2
1
x  xo  voxt  axt 2
2
vx  vox  axt
2
vx2  vox
 2ax x  xo 
 vx 
Uniform
circular
motion:
v2
ar 
r
Quadratic
formula
x
Newton’s
2nd Law
Fx = max
Friction
Ff = N
Restoring
Force
(Hooke’s
Law)
v f  vi
x  xo  vx  t
2
 b  b 2  4ac
2a
Fy = may
Fs  k    o
Fx  kx
6
Fz = maz
Work &
Energy
Mechanical
Energy
Impulse &
Momentum
Rocket
angular
motion
constant
angular
acceleration
angular
momentum
W = Fdcos()
K
U spring
E  Wnonconservative  I
 

J  F  t  p


p  mv
vector version


dv  dm
Fext  m
V
dt
dt
dm
0
dt

 
t
v
a
s

 t
 t
r
r
r
 = o + t

t
Universal
Gravitation
Fg 
dv x
dm
 ve , x
dt
dt
1
 I 2
2
Moment of Inertia
for a particle about
a point: I  mr 2
 2   o2  2  


L  I
  I

static equilibrium  F  0 &
rigid body

dL
 
dt

GM m
r2
G  6.67  10 11
Fext , x  m
Kr 
 = o + ot + (1/2)t2
  
Lrp
torque
1
2
k l  l o 
2
1
 kx 2
2
No external force :


p final  pinitial
one dimensional
as in the text
dm
ve  0 ;
0
dt
 
1 2
mv
2
U spring 
E=K+U
kinetic energy
1
K  I 2
2
  
  r F
Simple
Harmonic
Motion
Wtotal = K;
Wconservative = -U
Ug = mgy
or
U  mgh
Ug  
GM m
r
ve 
2GM
R
N  m2
kg 2
x  A cos t   
  2f
spring:
7

k
m
pendulum:
g




0