Physics 103
Exam IVb
8 December 2010
Name ______________________________
Part A: Select and circle the best answer for each of the following questions:
[0 or 1 point each]
1.
The time rate of change in angular velocity is defined to be the
a) angular acceleration
b) angular momentum
c) moment of inertia
d) angular velocity
2.
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
3.
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
4.
The “correct” plural of pendulum is ________________.
a) pendulums
b) pendulae
c) pendula
d) penduluses
5.
The SI units of angular torque are _________________.
a) kg m2/s
b) N m
c) N/m
d) kg m/s2
Part B: Solve the following problems. Show your work. [0, 1, or 2 each]
6.
A simple pendulum swings at a frequency of 5 Hz. How long is the pendulum?
7.
What is the magnitude of the torque exerted by the wrench on the nut?
1
8.
A force F = 100 N presses a brake pad against the edge of a spinning disk. The axis of rotation
is perpendicular to the plane of the disk, through its center. The coefficient of friction between
the pad and the disk is  = 0.4. 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?
9.
A 900 kg car drives with constant speed (10 m/s) around a horizontal circle of radius 50 m.
What is the car’s angular speed around the center of the circle?
10. A car wheel rolls without sliding at a speed of 3.00 m/s. The mass of the wheel is 5.00 kg and
its radius is 0.15 m. Compute the rotational kinetic energy of the wheel.
1
[The moment of inertia of a disk is MR 2 ]
2
2
11. 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.
12. 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!]
13. 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
14. 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.
15. Compute the moment of inertia of this system of three masses, about the z-axis.
[M1 = 2 kg; M2 = 4kg; M3 = 1 kg]



[ r1  ( 0,0 ); r2  ( 3m,0 ); r3  ( 0,3m ) ]
4
Part C: Work the following problem. Show your work, and use words
and phrases to describe your reasoning. [10 points]
16. An ideal string is wrapped around a pulley. Hanging from the free end
of the string is a mass, m = 4.0 kg. The axle of the pulley is frictionless,
but the string does not slip on the pulley. Calculate the acceleration of
1
the mass, m. M = 10.0 kg and R = 0.5 m and I  MR 2 . Don’t forget
2
the free body diagrams.
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 
v f  vi
2
Uniform
circular
motion:
ar 
v2
r
Quadratic
formula
x
 b  b 2  4ac
2a
Newton’s
2nd Law
Fx = max
Friction
Ff = N
Restoring
Force
(Hooke’s
Law)
x  xo  vx  t
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 
 = o + ot + (1/2)t2
rigid body
static equilibrium
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

F  0 &

dL
 
dt

GM m
r2
G  6.67  10 11
Fext , x  m
Kr 
  
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
Waves
y  A coskx   t 
k
8
2

  2 f
wave speed:
c f