Exam 3 is at 7 pm tomorrow
Conflict is at 5:15 pm in 151 Loomis
There are extra office hours today & tomorrow
This morning’s HW deadline moved to Friday
(80% deadline not moved – still next Tuesday)
A ladder of weight 60 N leans against a frictionless wall
at an angle of q = 70o as shown in the figure. Friction between the
floor and the ladder keeps it from slipping
. What is the magnitude of the force of friction, Ff, between the floor and the ladder?
a.
b.
c.
d.
e.
Ff = 5.0 N
Ff = 11. N
Ff = 15. N
Ff = 29. N
Ff = 60 N
2. If the angle of the ladder were decreased from 70o to 50o, the force of friction required
to keep the ladder from slipping would
a. increase
b. decrease
c. remain the same
Consider a student rotating on a stool with angular speed , holding weights in her
outstretched hands. If she drops one of the weights to the ground, her angular speed
will
a. increase
b. stay the same
c. decrease
4. Now consider a student rotating on a stool with angular speed  with no weights in
her hands. Suppose someone drops (vertically) a small weight into her horizontally
outstretched hand. Her angular speed will
a. increase
b. stay the same
c. decrease
A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular
bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely
about a pivot at its center. The gum sticks to the end of the bar and the angular speed of
the bar just after the collision is measured to be  = 3 rad/s. Assume that the wad of
gum is a point particle and assume that the pivot is frictionless.
(You do not have to worry about gravity in this problem)
5. What is the magnitude of the angular momentum of the gum with respect to the
pivot before it collides with the bar?
a. 0 kg m2 /s
b. 0.48 kg m2 /s
c. 1.12 kg m2 /s
A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular
bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely
about a pivot at its center. The gum sticks to the end of the bar and the angular speed of
the bar just after the collision is measured to be  = 3 rad/s. Assume that the wad of
gum is a point particle and assume that the pivot is frictionless.
(You do not have to worry about gravity in this problem)
6. What is the angular momentum of the gum with respect to the pivot after it collides
with bar?
a. 0.29 kg m2 /s
b. 0.48 kg m2 /s
c. 1.12 kg m2 /s
A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular
bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely
about a pivot at its center. The gum sticks to the end of the bar and the angular speed of
the bar just after the collision is measured to be  = 3 rad/s. Assume that the wad of
gum is a point particle and assume that the pivot is frictionless.
(You do not have to worry about gravity in this problem)
7. What is the mass of the bar?
a.
b.
c.
d.
e.
1.7 kg
2.0 kg
2.3 kg
3.1 kg
5.2 kg
The axle of a spinning disk of mass m is placed upon a single fixed support as shown
below. The disk’s angular velocity vector  is indicated in the figure, as is the
gravitational force on the disk.

L
pivot
mg
8. Which of the following figures accurately shows the motion of the spinning disk?
a. As viewed from above, the disk precesses clockwise:

pivot
mg
b. As viewed from above, the disk precesses counter-clockwise.

pivot
mg
c. The disk does not fall and does not precess.

pivot
mg
A skater spins about a fixed point on the ice. She begins with her arms extended and an
initial angular velocity 0. She then pulls her arms in to her body. After her arms are
pulled to her body, she spins with an angular velocity f. Throughout the time she is
spinning, no external forces are acting in the horizontal plane.
9. How do the magnitudes of the initial and final angular velocities compare?
a. 0 > f
b. 0 = f
c. 0 < f
10. Which one of the following statements is true?
a. The angular momentum of the skater remains constant.
b. The moment of inertia of the skater remains constant.
c. Both the angular momentum and the moment of inertia of the skater change.
11. The kinetic energy of the skater
a. increases because the skater does work.
b. decreases because the skater does work.
c. stays the same because the skater does no work.
A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with
a frictionless pivot and a string as shown in the diagram above. The initial angle
of the rod with respect to the wall, , is 39. The string is then cut. The moment
of inertia of a rod about an axis through one end is 1/3ML2.
12. What is the angular acceleration of the rod, , immediately after the string
is cut?
a.
b.
c.
d.
e.
 = 1.75 rad/s2
 = 3.09 rad/s2
 = 4.92 rad/s2
 = 6.17 rad/s2
 = 7.84 rad/s2
13. What is the angular velocity  of the rod when it is horizontal (=90)
a. 1.4 rad/sec
b. 3.1 rad/sec
c. 3.9 rad/sec

A disk of radius R, mass M, and moment of inertia I = (1/2)MR2 rolls without slipping
down an incline and onto a horizontal table. The disk then continues to the right and goes
up a frictionless ramp. The disk starts at rest at a height h above the table, as shown
14. What is the speed of the center of mass of the disk when it reaches the bottom of the
ramp?
a.
b.
c.
2 gh
4 gh
3
10 gh
7
d.
gh
e.
Mgh
15. What is the maximum height above the table that the disk reaches on the frictionless ramp?
a. less than h
b. h
c. greater than h
A disk has mass M = 1.0 kg and radius, R = 0.1 m is
free to rotate about a fixed axle through its center.
Since the axle is fixed, the center of mass of the disk
does not move. The disk is initially not rotating. A
student wraps a string 12 times around the perimeter
of the disk and then pulls the string with a constant
force of F = 1.0 N, as shown in the figure below
16. The student pulls on the string until it is completely unwound, and the string does
not slip on the disk as it is pulled. After the string has unwound, what is the angular
speed of the disk  :
a.
b.
c.
d.
e.
 = 6.3 radians/sec
 = 17.6 radians/sec
 = 26.4 radians/sec
 = 32.8 radians/sec
 = 54.9 radians/sec
A disk has mass M = 1.0 kg and radius, R = 0.1 m is
free to rotate about a fixed axle through its center.
Since the axle is fixed, the center of mass of the disk
does not move. The disk is initially not rotating. A
student wraps a string 12 times around the perimeter
of the disk and then pulls the string with a constant
force of F = 1.0 N, as shown in the figure below
17. Now suppose the student repeats the experiment, this time wrapping the string
around the perimeter of the disk 6 times and pulling the string with a constant force of
F = 2.0 N. As before, the disk is initially not rotating. How does the angular speed of
the disk after the string unwinds, , compare to  found in the previous problem?
a.  < 
b.  = 
c.  > 
A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is
pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a
vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its
inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is
observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of
inertia for the spool is given by 1/2MR2)
Top
View
M
R
ACM =2.1 m/s
r
2
Side
View
F
F= 15 N
Frictionless Table
18. What is the mass of the disk M?
a. 2.75 kg
b. 5.28 kg
c. 7.14 kg
A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is
pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a
vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its
inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is
observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of
inertia for the spool is given by 1/2MR2)
Top
View
M
R
ACM =2.1 m/s
r
2
Side
View
F
F= 15 N
Frictionless Table
19. What is the angular acceleration of the disk ?
a.
b.
c.
d.
e.
2.8 rad/s2
4.7 rad/s2
8.4 rad/s2
3.3 rad/s2
7.1 rad/s2
A Physics 211 student is out shoveling snow in the driveway. At one point he holds
the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without
moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the
right, and the center of mass of the snow is 0.5 meters further to the right as shown
in the figure below. Gravity acts in the –y direction.
20. Assuming the shovel is massless, what is the y-component Fy of the force
that his left hand exerts on the shovel?
a. Fy = –35 N
b. Fy = –10 N
c. Fy = 0 N
d. Fy = 10 N
e. Fy = 35 N
A Physics 211 student is out shoveling snow in the driveway. At one point he holds
the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without
moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the
right, and the center of mass of the snow is 0.5 meters further to the right as shown
in the figure below. Gravity acts in the –y direction.
21. Now suppose that the handle of the shovel has a mass of 1 kg, uniformly distributed
along its 1.2 meter length. Taking into account the mass of the handle, the magnitude of the
force of the student’s left hand on the end of the shovel’s handle will
a. increase.
b. decrease.
c. stay the same.
Two blocks are suspended over a pulley by a string of negligible mass as shown below. The
block on the left has a mass of m1, and the block on the right has mass m2. The pulley is a
uniform solid cylinder with mass M and radius R. The block on the right has a downward
acceleration equal to 1/3 the acceleration due to gravity. The tension in the string supporting
the mass on the left is T1 = 170N and the tension in the string supporting the mass on the right
is T2 = 255N. The string does not slip on the pulley.
22. What is the mass, m2, of the block on the right?
M
R
a. m2 = 43 kg
b. m2 = 39 kg
c. m2 = 26 kg
T1=170N
T2=255N
m1
m2
23. What is the mass, M, of the pulley?
a.
b.
c.
d.
e.
M = 14 kg
M = 27 kg
M = 39 kg
M = 46 kg
M = 52 kg
a =g/3
24. A judge’s gavel has a mass of 0.7 kg and has a moment of inertia of 0.10 kg m2
around an axis through its center of mass, perpendicular to the paper in the drawing
above. The distance between the center of mass of the gavel and the end of the handle
is 30 cm. What is the moment of inertia of the gavel around an axis through the end of
the handle, perpendicular to the paper?
a.
b.
c.
d.
e.
0.05 kg m2
0.10 kg m2
0.16 kg m2
0.20 kg m2
0.31 kg m2