True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 99.
The exam period was 90 minutes; the average score was 76.6; the median
score was 82. Click here to see the formula
sheet that came with the exam.
A ladder of weight 60 N leans against a frictionless wall at an angle
of θ = 70° 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) Ff = 5 N
(b) Ff = 11 N
(c) Ff = 15 N
(d) Ff = 29 N
(e) Ff = 60 N
(c) remain the same.
Consider a student rotating on a stool with angular speed
ω, holding weights in her outstretched hands. If she drops
one of the weights to the ground, her angular speed will
(b) stay the same.
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
ω = 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)
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) 0.29 kg m2/s
(b) 0.48 kg m2/s
(c) 1.12 kg m2/s
(a) 1.7 kg
(b) 2.0 kg
(c) 2.3 kg
(d) 3.1 kg
(e) 5.2 kg
Which of the figures at right accurately shows the motion of the
A skater spins about a fixed point on the ice. She begins with her
arms extended and an initial angular velocity
ω0. She then pulls her arms in to her body.
After her arms are pulled to her body, she spins with an angular
velocity ωf. Throughout the time she is
spinning, no external forces are acting in the horizontal plane.
How do the magnitudes of the initial and final angular velocities
(a) ω0 > ωf
(b) ω0 = ωf
(c) ω0 < ωf
(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.
(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 θ 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
What is the angular acceleration α of the rod immediately
after the string is cut?
(a) α = 1.75 rad/s2
(b) α = 3.09 rad/s2
(c) α = 4.92 rad/s2
(d) α = 6.17 rad/s2
(e) α = 7.84 rad/s2
(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 = MR2/2 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.
Which one of the choices at right is an expression for the speed of
the center of mass of the disk when it reaches the bottom of the
(a) less than 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.
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 ω of the disk?
(a) ω = 6.3 radians/sec
(b) ω = 17.6 radians/sec
(c) ω = 26.4 radians/sec
(d) ω = 32.8 radians/sec
(e) ω = 54.9 radians/sec
(a) ω' < ω
(b) ω' = ω
(c) ω' > ω
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
What is the mass M of the disk?
(a) 2.75 kg
(b) 5.28 kg
(c) 7.14 kg
(a) 2.8 rad/s2
(b) 4.7 rad/s2
(c) 8.4 rad/s2
(d) 3.3 rad/s2
(e) 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 0.7 m 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.
Assuming the shovel is massless, what is the y-component
Fy of the force that his left hand exerts on the
(a) Fy = -35 N
(b) Fy = -10 N
(c) Fy = 0 N
(d) Fy = 10 N
(e) Fy = 35 N
(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 =
170 N and the tension in the string supporting the mass on the right is
T2 = 255 N. The string does not slip on the pulley.
What is the mass m2 of the block on the
(a) m2 = 43 kg
(b) m2 = 39 kg
(c) m2 = 26 kg
(a) M = 14 kg
(b) M = 27 kg
(c) M = 39 kg
(d) M = 46 kg
(e) M = 52 kg
(a) 0.05 kg m2
(b) 0.10 kg m2
(c) 0.16 kg m2
(d) 0.20 kg m2
(e) 0.31 kg m2