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 110.
The exam period was 90 minutes; the average score was 71.1; the median
score was 74. Click here to see the formula
sheet that came with the exam.
A mass M hangs from the end of a rod of mass m and
length L. The rod is held in place with a hinge attached to a
wall on the right, and it has a cable with a tension which is measured
to be T.
What is the value of M, in terms of m,
L,T and θ ?
(a) M = (T / (gsinθ)) - m/2
(b) M = (T sinθ/g) - m/2
(c) M = m tanθ (T / g - m) / (T/g + m)
(d) M = T cosθ + mg
(e) M = m sinθ + T / g
(b) stays the same.
A solid cylinder (I = 1/2 MR2) and a solid
sphere (I = 2/5 MR2), of the same radius and
mass, roll down an incline of angle θ = 30°. They both
start from rest at a distance D = 2 meters up the incline, as
shown in the diagram, and roll without slipping to the bottom of the
The initial gravitational potential energy of the two objects is
partially lost in work done overcoming frictional forces as the objects
roll down the incline.
(a) larger for the solid sphere than it is for the solid cylinder.
(b) the same for both objects.
(c) smaller for the solid sphere than it is for the solid cylinder.
Four 1 kg-masses are held together in the form of a square by four
rigid, massless rods, each of length 2l. The positions of the
point masses are designated a, b, c and d, as shown in the diagram.
Axis AB lies in the plane formed by the square and passes through its
center. Axis CD is parallel to AB and passes through the masses c and
d. Axis XY is perpendicular to the plane of the square and passes
through its center, as shown on the right.
Compare the three moments of inertia of the square about the three
specified axes, IAB, ICD,
IXY. Which one of the following statements is
(a) IAB = ICD > IXY
(b) IAB < ICD < IXY
(c) IAB < ICD = IXY
(d) IAB > ICD < IXY
(e) IAB < ICD > IXY
(a) 14.7 kg l 2
(b) 18.6 kg l 2
(c) 19.2 kg l 2
(d) 21.7 kg l 2
(e) 24.9 kg l 2
A massless rope is holding a solid disk of mass M and radius
R (I = 1/2 MR2). The rope is attached
to the center of the disk and a frictionless, vertical wall as shown in
the figure. The center of the disk is at a distance L below where the
rope is attached to the wall.
What is the force exerted on the disk by the wall?
(a) Tdisk > Tsphere
(b) Tdisk = Tsphere
(c) Tdisk < Tsphere
Consider the earth as a uniform, solid sphere of radius
Re = 6.4 × 106 m with mass
Me = 6.4 × 1024 kg that makes one
complete revolution in 1 day (= 24 hours.) As part of a carefully
crafted attack, aliens from outer space drop a small neutron star on the
equator. The mass of the neutron star is Mn = 6.4
× 1024 kg, the same as the mass of the earth. (Assume
the neutron star is a point mass.)
After the mass is dropped, how long does it take the earth to make
one complete revolution?
(a) 0.93 days
(b) 1.00 days
(c) 2.00 days
(d) 2.67 days
(e) 3.50 days
(a) It would be less than with the star on the equator.
(b) It would be the same as with the star on the equator.
(c) It would be greater than with the star on the equator.
A spool with a thread wound around it is pulled with a force T
= 30 N as shown below. The total moment of inertia of the spool is
I = 1.25 kg·m2, its mass is M = 10 kg,
its outer radius is R = 0.5 m and its inner radius is r =
0.1 m. The spool rolls without slipping and starts from rest.
Find the angular acceleration α of the spool.
(a) α = 1.60 rad/s2
(b) α = 2.28 rad/s2
(c) α = 2.95 rad/s2
(d) α = 3.32 rad/s2
(e) α = 4.80 rad/s2
After the rockets shut off, what will be the rotational frequency of the
(a) ω = 0.078 rad/s
(b) ω = 0.90 rad/s
(c) ω = 1.59 rad/s
(d) ω = 2.20 rad/s
(e) ω = 2.74 rad/s
(a) L = 7 m
(b) L = 12 m
(c) L = 15 m
(d) L = 18 m
(e) L = 20 m
A piece of gum of mass m = 0.1 kg, is thrown at a bar of mass
M = 1 kg, and length d = 1 m, pivoted about its center and
initially at rest as shown. It sticks to the end of the bar and the
final angular speed of the bar is measured to be ω = 3
rad/s. Assume that the gum has a size much smaller than d.
What is the initial speed v of the gum?
(a) v = 3.7 m/s
(b) v = 4.8 m/s
(c) v = 5.2 m/s
(d) v = 5.9 m/s
(e) v = 6.5 m/s
(a) smaller than v.
(b) the same than v.
(c) larger than v.
Of the following choices, which best describes the approximate
location of the center of mass of the bar?
(a) At the junction between the dark-shaded and light-shaded pieces.
(b) At the pivot.
(c) In the light-shaded region, to the right of the pivot.
(a) |α1| = |α2|
(b) |α1| > |α2|
(c) |α1| < |α2|
Calculate the distance x if the
tension T1 in the first rope is measured to be 85 N.
(a) x = 0.44 m
(b) x = 0.36 m
(c) x = 0.80 m
(d) x = 0.60 m
(e) x = 0.25 m
A turntable has a mass of 1 kg and a radius of 0.17 m and is
initially rotating freely at 78 rpm (ωi,t =
8.168 rad/s). There are no external torques acting on the system. The
moment of inertia of the turntable can be approximated by that of a disk
(Idisk = MR2/2).
A small object, initially at rest, is dropped vertically onto the
turntable and sticks to the turntable at a distance d of 0.10 m
from its center as shown in the figure. When the small object is
rotating with the turntable, the angular velocity of the turntable
ωf,t is 72.7 rpm (7.613 rad/s). What is the
mass of the small object that was dropped onto the turntable?
(a) 0.048 kg
(b) 0.070 kg
(c) 0.086 kg
(d) 0.105 kg
(e) 0.123 kg
(a) 0.080 J
(b) 0.095 J
(c) 0.103 J
(d) 0.121 J
(e) 0.137 J
(a) less than that of placing the first record on the turntable.
(c) more than that of placing the first record on the turntable.