Spring 2010 Physics 211 Hour Exam 3
(24 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

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 102. The exam period was 90 minutes; the average score was 76.5; the median score was 81. Click here to see the formula sheet that came with the exam.


This and the next two questions refer to this situation:

A pair of forces, F1 and F2 of magnitude F is applied tangentially to a spool to create a torque about its symmetry axis as shown below. The spool has ends in the form of disks, each of mass M and radius R. The center of the spool is also a disk, with radius r and of negligible mass.

What is the moment of inertia Is of the spool about its axis of symmetry?

(a)   Is = Mr2
(b)   Is = MR2
(c)   Is = MR2 / 2


What is the acceleration α of the spool about its symmetry axis in terms of the momentum of inertia Is about that axis?

(a)   α = FR / Is
(b)   α = Fr / Is
(c)   α = 2Fr / Is


If the moment of inertia of the spool about its symmetry axis is Is, what is the moment of inertia IA of the spool about the axis A which is a distance 1.5R from the symmetry axis, as shown in the figure.

(a)   IA = Is + 9MR2 / 2
(b)   IA = Is + 3MR2 / 4
(c)   IA = Is + M(R2/4 + r2/4)
(d)   IA = Is + M(3R2/2 + r2/4)
(e)   IA = Is + 3MR2 / 2


This and the next question refer to this situation:

Consider the following simple object made up of two uniform spheres of radius r and mass m, connected by a massless stick. The three axes are mutually perpendicular. Axis "1" passes along the stick; axes "2" and "3" pass through the center of mass of the system.

What is the relationship among the three moments of inertia of the system, calculated with respect to the three axes, I1, I2 and I3?

(a)   I1 = I2 = I3
(b)   I1 < I2 < I3
(c)   I1 < I2 = I3


Initially the object is at rest. If a constant torque τ is applied to the object about axis 2 for a time t, then the angular momentum of the object is

(a)   t/τ about axis 2
(b)   t*τ about axis 2
(c)   t*τ about axis 1
(d)   t*τ*I2 about axis 2
(e)   τ*I2/t about axis 2


This and the next three questions refer to this situation:

Two masses, m1 = 3 kg and m2 = 2 kg, are suspended with a massless rope over a pulley of mass M = 10 kg. The pulley turns without friction and may be modeled as a uniform disk of radius R = 0.1 m. You may neglect the size of the masses. The rope does not slip on the pulley. The system begins at rest.

If m1 starts at a height h = 1 m above the ground, what is its speed v when it hits the ground?

(a)   v = 3.82 m/s
(b)   v = 2.97 m/s
(c)   v = 2.04 m/s
(d)   v = 1.40 m/s
(e)   v = 0.981 m/s


If the pulley were modeled as a hoop (cylindrical shell) rather than a solid disk but still with mass M = 10 kg the speed of m1 when it hits the ground would be

(a)   larger.
(b)   the same.
(c)   smaller.


As m1 falls, the work done on the pulley by the rope is

(a)   zero because the tension in each rope is the same so there is no torque.
(b)   greater than zero because its kinetic energy increases.
(c)   less than zero because the torque on the pulley and the angular displacement point in opposite directions.


The behavior of the angular displacement of the pulley as a function of time θ(t) is best represented by:



A uniform solid sphere rolls down a ramp without slipping. If it starts at rest, what is its speed when it reaches the bottom of the ramp 2 m below its starting point?

(a)   1.32 m/s
(b)   5.29 m/s
(c)   6.91 m/s
(d)   8.33 m/s
(e)   9.81 m/s


A disk is placed on a pivot through its center of mass, allowing it to rotate freely about an axis perpendicular to the disk. Three different sets of forces are applied to the disk, as shown. Which set of forces has the largest magnitude of the total torque about the pivot?



This and the next two questions refer to this situation:

A uniform beam of length L = 3 meters and mass M = 150 kg has a block of mass m = 300 kg and negligible size firmly attached to one end as shown below. The beam is attached by a hinge to the wall and extends perpendicularly from the wall. It is braced with a rope attached some distance away, which makes an angle θ = 30° with respect to the beam.

What is the tension T in the rope?

(a)   T = 3679 newtons
(b)   T = 4185 newtons
(c)   T = 6590 newtons
(d)   T = 7358 newtons
(e)   T = 8309 newtons


Taking the hinge as the axis of rotation, what is the direction of the torque on the beam caused by the tension in the rope?

(a)   along the beam, pointing in towards the hinge
(b)   up and to the right, perpendicular to the rope but in the plane of the page
(c)   out of the page.


The rope is cut. What is the magnitude |α| of the angular acceleration of the beam and block immediately after the rope is cut?

(a)   |α| = 1.00 radians/sec2
(b)   |α| = 1.83 radians/sec2
(c)   |α| = 2.10 radians/sec2
(d)   |α| = 2.71 radians/sec2
(e)   |α| = 3.50 radians/sec2


This and the next question refer to this situation:

A 25 kg boy sits on a see-saw with his 85 kg father. The see-saw consists of a 2 m long board of mass 20 kg and a fulcrum which can be placed anywhere along the board to provide the best balance. Neglect the sizes of the boy and his father.

When the see-saw is balanced, how far away is the boy from the fulcrum?

(a)   0.15 m
(b)   0.73 m
(c)   1.00 m
(d)   1.46 m
(e)   1.87 m


What is the magnitude of the force of the fulcrum on the see-saw?

(a)   441 N
(b)   833 N
(c)   1274 N


This and the next question refer to this situation:

The gyroscope pictured is turning such that the top of the wheel is coming out of the page, and the bar (which is attached to the center of mass of the gyroscope) is sitting on a fulcrum.

The angular momentum vector of the gyroscope points in which direction?

(a)   +x
(b)   -x
(c)   +z


The direction of rotation (precession) of the gyroscope (about the fulcrum) is

(a)   counterclockwise in the plane of the paper (rotating in the direction from the x axis to the y axis).
(b)   out of the paper (rotating in the direction from the x axis to the z axis).
(c)   into the paper (rotating in the direction from the x axis to the -z axis).


A yo-yo is falling under influence of gravity, while the free end of the string is being held steady by a Physics 211 student. The string is wound on the spool of the yo-yo with a constant radius r. The mass of the yo- yo is m and its moment of inertia is I. What is the magnitude of the downward acceleration a of the yo-yo?



This and the next two questions refer to this situation:

A bar of mass M = 2 kg and length L = 0.4 m lies at rest on a horizontal frictionless floor. One end of the bar is attached to a fixed frictionless pivot A.

A putty ball of mass m = 0.2 kg moving at a velocity of 2 m/s perpendicular to the bar strikes the other end of the bar and sticks to it as shown in the figure.

What is the angular velocity ω of the bar after the putty ball strikes it?

(a)   ω = 1.15 s-1
(b)   ω = 1.68 s-1
(c)   ω = 1.98 s-1
(d)   ω = 2.65 s-1
(e)   ω = 2.88 s-1


Suppose the experiment is repeated with a putty ball having half the mass and twice the initial velocity, but everything else is the same as above. How will the final angular velocity of the system in this case compare to the one you found above?

(a)   It will be bigger.
(b)   It will be the same.
(c)   It will be smaller.


Suppose the total kinetic energy of the putty plus bar is KE1 before the collision and KE2 after the collision. How do KE1 and KE2 compare?

(a)   KE1 > KE2
(b)   KE1 = KE2
(c)   KE1 < KE2


This and the next question refer to this situation:

A fly of mass 2 g (.002 kg - it's a big fly), viewed from above, begins to walk counter-clockwise on a turntable of mass 0.5 kg. The turntable is a uniform cylinder of radius 0.2 m that turns without friction about its center, and the fly is situated half way between the center and the outer radius of the cylinder. The fly and the turntable are initially at rest.

If the fly's speed is .005 m/s in its circular path (relative to the ground), what is the magnitude of the angular velocity of the turntable?

(a)   2.5 × 10-6 s-1
(b)   7.0 × 10-6 s-1
(c)   2.5 × 10-5 s-1
(d)   1.0 × 10-4 s-1
(e)   3.2 × 10-4 s-1


Now the fly stops walking. After the fly has stopped, the turntable is

(a)   still rotating clockwise.
(b)   not rotating at all.
(c)   rotating counter-clockwise.