Physics Midterm Exam

A thin rod 5.60 m long with mass 5.80 kg is rotated counterclockwise about an axis through its midpoint. It completes 3.70 revolutions every second. What is the magnitude of its angular momentum?

352 kgm/s²

An LP record rotates at 33 1/3 rpm (revolutions per minute) and is 12.0 inches in diameter. What is the angular velocity in rad/s for a fly sitting on the outer edge of an LP rotating in a clockwise direction?

-3.49 rad/s

A truck with a mass of 2200 kg is moving at a constant 13 m/s. A 920 kg car with the same momentum as the truck passes it at a constant speed. How fast is the car moving?

31 m/s

What is the angular displacement in radians that the minute hand of a watch moves through from 3:00 A.M. to 10:00 P.M. the same day? Express your answer to the nearest whole radian.

-119 rad

A CD is rotating counterclockwise at 30 rad/s. What angular acceleration will bring it to a stop in 30 rad?

-15 rad/s²

Ball A has mass 5.0 kg and is moving at −4.8 m/s when it strikes stationary ball B, which has mass 3.9 kg, in a head-on collision. If the collision is elastic, what is the velocity of ball A?

-0.59 m/s

During a snowball fight, two snowballs travelling towards each other collide head-on. The first is moving east at a speed of 16.1 m/s and has a mass of 0.450 kg. The second is moving west at 13.5 m/s and has a mass of 0.991 kg. When the snowballs collide, they stick together and travel west. What is the final velocity they travel while stuck together?

-4.26 m/s

Three railroad cars, each with mass 2.3×10⁴ kg, are moving on the same track. One moves north at 20 m/s, another moves south at 10 m/s, and third car between these two moves south at 10 m/s. When the three cars collide, they couple together and move with a common velocity. What is their velocity after they couple?

0 m/s

A weightlifter has been given a barbell to lift. One end has a mass of 7.7 kg while the other end has a mass of 4.7 kg. The bar is 0.20 m long. (Consider the bar to be massless, and assume that the masses are thin disks, so that their centers of mass are at the ends of the bar.) How far from the heavier end should she hold the bar so that the weight feels balanced?

0.076 m

Bob and Ray push on a door from opposite sides. They both push perpendicular to the door. Bob pushes 0.65 m from the door hinge with a force of 91 N. Ray pushes 0.59 m from the door hinge with a force of 100 N, in a manner that tends to turn the door in a clockwise direction. What is the net torque on the door?

0.15 Nm

A solid ball of mass 0.75 kg and radius 0.17 m is attached by a small loop on its surface to a string of length 0.29 m. You are whirling the ball around in a circle by holding the end of the string. What is the moment of inertia of the ball? You can assume that the mass of the string and loop are negligible, but the sphere is large enough compared to the string length that it should not be considered as a particle.

0.17 kgm²

A 3.6-meter long horizontal plank is held up by two supports. One support is at the left end, and the other is 0.90 m from the right end. The plank has uniform density and has a mass of 40 kg. How close can a 70 kg person stand to the unsupported end before causing the plank to rotate?

0.39 m

The net force on a baby stroller increases at a constant rate from 0 N to 80 N, over a period of 0.075 s. The mass of the baby stroller is 7.4 kg. It starts stationary; what is its speed after the 0.075 s the force is applied?

0.41 m/s

A runner rounds a circular curve of radius 27.0 m at a constant speed of 5.25 m/s. What is the magnitude of the runner's centripetal acceleration?

1.02 m/s²

A horizontal log just barely spans a river, and its ends rest on opposite banks. The log is uniform and weighs 2400 N. If a person who weighs 840 N stands one fourth of the way across the log from the left end, how much weight does the bank under the right end of the log support?

1.4 x 10³ N

Two children sit 2.60 m apart on a very low-mass horizontal seesaw with a movable fulcrum. The child on the left has a mass of 30.0 kg, and the child on the right has a mass of 40.0 kg. At what distance, as measured from the child on the left, must the fulcrum be placed in order for them to balance?

1.53 m

What is the magnitude of angular momentum of a 1070 kg car going around a circular curve with a 10.0 m radius at 18.0 m/s? Assume the origin is at the center of the curve's arc.

1.93 x 10⁵ kgm/s²

Four balls are connected by a straight rod. One end of the rod is painted blue. The first ball has mass 1.0 kg and is 1.0 m from the blue end of the rod, the second ball has mass 2.0 kg and is 2.0 m from the blue end, and so on for the other two balls. The mass of the rod is negligible compared to the mass of the balls. What is the moment of inertia of this system for an axis of rotation perpendicular to the rod and touching the blue end?

100 kgm²

Lisa Marie is late to a party. She jumps into her sporty coupe and starts driving. Eventually she comes to a level curve, with a radius of 20 meters. What is the top speed at which she can drive successfully around the curve? The coefficient of static friction between the tires and the road is 0.7.

11.7 m/s

An electric drill delivers a net torque of 15.0 N∙m to a buffing wheel used to polish a car. The buffing wheel has a moment of inertia of 2.30×10⁻³ kg∙m2. At 0.0220 s after the drill is turned on, what is the angular velocity of the buffing wheel?

143 rad/s

In an automobile, the crankshaft transfers energy from the engine to the transmission, which in turn rotates the wheel axle. A particular car is rated at 126 hp ( = 9.40×10⁴ W), which you can take as the rate of energy transfer by the crankshaft when rotating at its maximum of 6060 revolutions per minute. What torque does the crankshaft supply?

148 Nm

A sport utility vehicle is traveling at a speed of 20.0 m/s. If its momentum has a magnitude of 32,800 kg∙m/s, what is the SUV's mass?

1640 kg

At a circus animal training facility, a monkey rides a miniature motorscooter at a speed of 7.0 m/s. The monkey and scooter together have a mass of 29 kg. Meanwhile, a chimpanzee on roller skates with a total mass of 55 kg moves at a speed of 1.5 meters per second. The magnitude of the momentum of the monkey plus scooter is how many times the magnitude of the momentum of the chimpanzee plus skates?

2.5

A child pushes a merry-go-round with a force of 50.0 N at an angle tangent to the circle (that is, perpendicular to a radius). If the child pushes it through exactly one full circle, and the merry-go-round has a radius of 1.15 m, how much work does she do?

361 J

How far is the center of mass of the Earth-Moon system from the center of the Earth? The Earth's mass is 5.97×10²⁴ kg, the Moon's mass is 7.4×10²² kg, and the distance between their centers is 3.8×108 m.

4.7 x 10⁶ m

Two cars are traveling around a circular track. The angle between them, from the center of the circle, is 50° and the track has a radius of 50 m. How far apart are the two cars, as measured around the curve of the track?

44 m

A hollow closed cylinder of radius R is rolling without slipping. (Think of an empty tin can.) Each of the two endcaps has a mass of M, and the rest (the hollow tube) has a mass of 3M, for a total object mass of 5M. What is the ratio of linear kinetic energy to rotational kinetic energy?

5/4

A hollow glass holiday ornament in the shape of a sphere is suspended on a string that forms an axis of rotation through the ornament's center. If the ornament has mass 0.0075 kg and radius 0.035 m, what is its moment of inertia for an axis that passes through its center?

6.13 x 10⁻⁶ kgm²

A 7.75 kg solid ball with a radius of 0.185 m rolls without slipping at 3.55 m/s. What is its total kinetic energy?

68.4 J

You want to exert a torque of at least 50.0 N∙m on a wrench whose handle is 0.150 m long. If you can provide a force of 355 N to the end of the wrench, what is the minimum angle at which you can apply the force in order to achieve the desired torque?

69.9°

A ball with mass 0.48 kg moves at a constant speed. A centripetal force of 23 N acts on the ball, causing it to move in a circle with radius 1.7 m. What is the speed of the ball?

9.0 m/s

Saturn travels at an average speed of 9.66×103 m/s around the Sun in a roughly circular orbit. Its distance from the Sun is 1.43×10¹² m. Which equation do you use to find out how long (in seconds) a "year" is on Saturn?

T = 2πr/v

Your coffee cup is initially stationary. You and your pet chimpanzee are trying to rotate the coffee cup in opposite directions. You exert a torque of -25 Nm, and your chimpanzee exerts a torque of +20 Nm. Would expect the cup to start rotating clockwise or counterclockwise?

clockwise

The blades of a kitchen blender rotate counterclockwise at 2.2×10⁴ rpm (revolutions per minute) at top speed. It takes the blender 3.2 seconds to reach this top speed after being turned on. What is the average angular acceleration of the blades?

~ 7.2 x 10² rad/s²