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 F_{f} between the floor and the ladder?

(a) F_{f} = 5 N (b) F_{f} = 11 N (c) F_{f} = 15 N (d) F_{f} = 29 N (e) F_{f} = 60 N

(a) increase. (b) decrease. (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

(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 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 m^{2}/s (b) 0.48 kg m^{2}/s (c) 1.12 kg m^{2}/s

(a) 0.29 kg m^{2}/s (b) 0.48 kg m^{2}/s (c) 1.12 kg m^{2}/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 spinning disk?

(a) (b) (c)

A skater spins about a fixed point on the ice. She begins with her arms extended and an initial angular velocity ω_{0}. She then pulls her arms in to her body. After her arms are pulled to her body, she spins with an angular velocity ω_{f}. 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 compare?

(a) ω_{0} > ω_{f} (b) ω_{0} = ω_{f} (c) ω_{0} < ω_{f}

(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 ML^{2}/3.

What is the angular acceleration α of the rod immediately after the string is cut?

(a) α = 1.75 rad/s^{2} (b) α = 3.09 rad/s^{2} (c) α = 4.92 rad/s^{2} (d) α = 6.17 rad/s^{2} (e) α = 7.84 rad/s^{2}

(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 = MR^{2}/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 ramp?

(a) (b) (c) (d) (e)

(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.

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·m^{2}, 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/s^{2}. (Note, you should not assume the moment of inertia for the spool is given by MR^{2}/2.)

What is the mass M of the disk?

(a) 2.75 kg (b) 5.28 kg (c) 7.14 kg

(a) 2.8 rad/s^{2} (b) 4.7 rad/s^{2} (c) 8.4 rad/s^{2} (d) 3.3 rad/s^{2} (e) 7.1 rad/s^{2}

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 F_{y} of the force that his left hand exerts on the shovel?

(a) F_{y} = -35 N (b) F_{y} = -10 N (c) F_{y} = 0 N (d) F_{y} = 10 N (e) F_{y} = 35 N

(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 m_{1}, and the block on the right has mass m_{2}. 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 T_{1} = 170 N and the tension in the string supporting the mass on the right is T_{2} = 255 N. The string does not slip on the pulley.

What is the mass m_{2} of the block on the right?

(a) m_{2} = 43 kg (b) m_{2} = 39 kg (c) m_{2} = 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 m^{2} (b) 0.10 kg m^{2} (c) 0.16 kg m^{2} (d) 0.20 kg m^{2} (e) 0.31 kg m^{2}