Name (Print): _______________________________ 4 Digit ID:________ Section: ______
A
 First, write your name and section number on both the Scantron card and this exam sheet.
 Use the formula sheet (last exam booklet page) and no other materials.
 Budget your time. There are 10 multiple choice problems and 2 long problems.
 For the long workout problems, you must show how you got your answers on this set of exam sheets.
Use the backs of pages if necessary. For most, if not all, of the multiple choice problems, it will be difficult to arrive at the correct answer without showing your work. However, while partial credit will be awarded for the long workout problems, partial credit will not be awarded on the multiple choice problems.
 Answer each question on the Scantron card using #2 pencil. Also circle your answers on question papers.
 Do not hesitate to ask for clarification of any exam question, if needed, from your proctor or Professor.
____________________________________________________________________________________
1 .
A wheel rotating about a fixed axis has an angular position given by

= 3.0

2.0t
3 , where

is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s?
A) 
1.0 rad/s 2
B) 
24 rad/s 2
C) 
2.0 rad/s 2
D) 
4.0 rad/s 2
E) 
3.5 rad/s 2 cE
2.
The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of
51° with the horizontal. If a person (mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the cable?
A) 0.83 kN
B) 0.30 kN
C) 0.38 kN
D) 0.42 kN
E) 3.0 kN
3.
Three forces F
1
= 2.0 N, F
2
= 12.0 N and F
3
= 5.0 N are applied to a rod, as shown in figure. What is the net torque about point O . The rod and three forces are in the plane of the page.
A) 95 Nm
B) 22 Nm
C) 14 Nm
D) 7 Nm
E) 2 Nm

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4. The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and
L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.
A) 18 J
B) 15 J
C) 12 J
D) 23 J
E) 26 J
5. A uniform beam of length 5.5 m and negligible mass is attached to the vertical wall and supports a 120 kg ball as shown in the figure. If θ
1
= 38 0 and θ
2
= 42 0 what is the tension T in the cable?
A) 146 N
B) 292 N
C) 342 N
D) 514 N
E) 735 N
6.
The dumbbell in the figure consists of a uniform rod (whose mass we can neglect) with a ball (a point mass) attached to each end. We can neglect the rotational inertia of the rod itself. Each ball (m = 4.0 kg) is located 2.0 meters from the center point "O" of the rod.
What angular acceleration (in radians/s 2 ) will a force F = 128 N produce?
A) 4
B) 8
C) 16
D) 32
E) 64
SAA
A
7.
The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest
in 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.
A) 12 rad
B) 8.0 rad
C) 10 rad
D) 16 rad
E) 6.8 rad
8. A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam (resultant force of the horizontal and vertical components)?
A) 0.68 kN
B) 0.57 kN
C) 0.74 kN
D) 0.63 kN
E) 0.35 kN

9.
Three objects of equal mass - a solid sphere, a solid cylinder, and a thin-shelled hollow cylinder - are placed at the top of an incline. All of the objects have the same radius. They are all released from rest at the same elevation and roll without slipping.
Which object reaches the bottom first?
A) The solid sphere
B) The solid cylinder
C) The hollow cylinder
D) They take the same time
E) Need more information
10.
A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s 2 . At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration (i.e., tangential and radial) of a point on the rim of the wheel?
A) 0.40 m/s 2
B) 0.29 m/s 2
C) 0.69 m/s 2
D) 0.49 m/s 2
E) 0.35 m/s 2
11. A 20 kg traffic lights are suspended from cables as shown. If

= 25 0
.
What is the magnitude of tension T
1
?
A) 120 N
B) 165 N
C) 196 N
D) 220 N
E) 420 N
12.
The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.
A) 2.9 J
B) 2.6 J
C) 3.1 J
D) 3.4 J
E) 1.6 J
13.
A massless rope is wrapped around a uniform cylinder that has radius R and mass M , as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is
A) (2/3)g
B) (1/2) g
C) (1/3) g
D) (1/6) g
E) (5/6) g

14.
A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.
A) 74 cm
B) 70 cm
C) 65 cm
D) 86 cm
E) 62 cm
15. 15.
Two blocks, m
1
= 1.0 kg and m
2
= 2.0 kg, are connected by a light string passing over a pulley. The pulley has a radius of 1.0 m and a moment of inertia of 5.0 kg.m
2 about its axis of rotation. The string does not slip on the pulley, and the system is released from rest. After the block m
2
descends through a distance of 5.0 m, what is the magnitude of the angular velocity of the pulley at that time? Use principle of conservation of energy in solving this problem.
A) 6.1 rad/s
B) 5.3 rad/s
C) 4.9 rad/s
D) 3.5 rad/s
E) 0 rad/s
16.
A puck of mass m = 0.5 kg is attached to a taut cord passing through a small hole on a frictionless, horizontal surface.
The puck is initially orbiting with a speed of 2 m/s in a circle of a radius of 0.2 m. The cord is then slowly pulled from below, decreasing the radius of the circle. What is the magnitude of the tension force in the cord when the radius of the circle decreases to 0.1 m?
A) 80 N
B) 40 N
C) 20 N
D) 10 N
E) 5 N
17. A uniform rod of mass M = 1.2 kg and length L = 0.80 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by (1/3) ML 2 . If a force
(F = 5.0 N,

= 40

) acts as shown, what is the resulting angular acceleration about the pivot point?
A) 16 rad/s 2
B) 12 rad/s 2
C) 14 rad/s 2
D) 10 rad/s 2
E) 33 rad/s 2
18.
The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W stands for the weight. In which diagram(s) is(are) the wheel in equilibrium?
A) A
B) B
C) C
D) D
E) A and C
.