A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length?

A) 2

B) 4

C)

D) 1

E) 1/2

B) 4

Initially, a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of the rock was 5.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m?

A) 3.9 m/s

B) 9.3 m/s

C) 15 m/s

D) 225 m/s

C) 15 m/s

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. What is the angular speed of the merry-go-round right after the two people have stepped on?

A) 0.20 rad/s

B) 0.40 rad/s

C) 0.60 rad/s

D) 0.80 rad/s

E) 0.67 rad/s

B) 0.40 rad/s

A 40.0-kg child running at 3.00 m/s suddenly jumps onto a stationary playground merry-go-round at a distance 1.50 m from the axis of rotation of the merry-go-round. The child is traveling tangential to the edge of the merry-go-round just before jumping on. The moment of inertia about its axis of rotation is 600 kg ∙ m2 and very little friction at its rotation axis. What is the angular speed of the merry-go-round just after the child has jumped onto it?

A) 0.788 rad/s

B) 0.261 rad/s

C) 6.28 rev/s

D) 2.00 rad/s

E) 3.14 rev/s

B) 0.261 rad/s

A light-weight potter's wheel, having a moment of inertia of is spinning freely at 40.0 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm, what is the mass of the clay?

A) 4.2 kg

B) 2.8 kg

C) 3.7 kg

D) 4.6 kg

A) 4.2 kg

A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is open and at rest. A small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. What is the angular speed of the door just after the collision with the ball?

A) 0.127 rad/s

B) 0.925 rad/s

C) 1.14 rad/s

D) 2.28 rad/s

E) 4.57 rad/s

C) 1.14 rad/s

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2. If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m2, what will be his new angular speed?

A) 2.25 rad/s

B) 4.60 rad/s

C) 6.25 rad/s

D) 0.81 rad/s

C) 6.25 rad/s

An ice skater has a moment of inertia of 5.0 kg ∙ m2 when her arms are outstretched, and at this time she is spinning at 3.0 rev/s. If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m2, how fast will she be spinning?

A) 2.0 rev/s

B) 3.3 rev/s

C) 7.5 rev/s

D) 10 rev/s

D) 10 rev/s

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s. What is the magnitude of the angular momentum of the stick?

A) 0.0394 kg ∙ m2/s

B) 0.473 kg ∙ m2/s

C) 0.0739 kg ∙ m2/s

D) 0.158 kg ∙ m2/s

E) 0.0236 kg ∙ m2/s

A) 0.0394 kg ∙ m2/s

A uniform, solid, cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at What is the magnitude of the flywheel's angular momentum?

A) 40 kg ∙ m2/s

B) 20 kg ∙ m2/s

C) 80 kg ∙ m2/s

D) 60 kg ∙ m2/s

A) 40 kg ∙ m2/s

Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system.

A) 1020 kg ∙ m2/s

B) 1500 kg ∙ m2/s

C) 975 kg ∙ m2/s

D) 940 kg ∙ m2/s

A) 1020 kg ∙ m2/s

In a certain cyclotron, a proton of mass 1.67 × 10-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 106 rad/s. What is the angular momentum of the proton?

A) 1.3 × 10-21kg ∙ m2/s

B) 1.8 × 10-21kg ∙ m2/s

C) 2.1 × 10-21kg ∙ m2/s

D) 3.2 × 10-21kg ∙ m2/s

C) 2.1 × 10-21kg ∙ m2/s

Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of 24 kg . m/s, and Fido runs northward with momentum 10 kg . m/s. They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision?

A) 14 kg . m/s

B) 26 kg . m/s

C) 34 kg . m/s

B) 26 kg . m/s

A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the direction of motion of the cars after collision?

A) 36.9° S of E

B) 36.9° E of S

C) 53.1° S of E

D) 53.1° E of S

C) 53.1° S of E

A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the speed of the cars after collision?

A) 8.3 m/s

B) 14 m/s

C) 17 m/s

D) 22 m/s

B) 14 m/s

A 900-kg car traveling 30.0° south of east at 12.0 m/s suddenly collides with a 750-kg car traveling north at 17.0 m/s. The cars stick together after colliding. What is the speed of the wreckage just after the collision?

A) 7.21 m/s

B) 12.2 m/s

C) 20.4 m/s

D) 25.0 m/s

E) 17.3 m/s

A) 7.21 m/s

A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. In what direction does the wreckage move just after the collision?

A) 36.9° N of E

B) 42.0° N of E

C) 45.0° N of E

D) 53.1° N of E

E) 48.0° N of E

E) 48.0° N of E

A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. What is the speed of the wreckage just after the collision?

A) 6.10 m/s

B) 12.2 m/s

C) 25.0 m/s

D) 35.0 m/s

E) 17.3 m/s

B) 12.2 m/s

A puck with a mass *m*1 = 50 g moving at 1.0 m/s approaches a
stationary puck with a mass *m*2 = 100 g on a frictionless air
table, and they undergo a sudden two-dimensional elastic collision.
After the collision, both pucks have identical speeds, but travel in
different directions. What is the angle between the original and final
paths of puck with mass *m*1?

A) 30°

B) 60°

C) 90°

D) 120°

E) 150°

C) 90°

A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at at 15° north of east just after the collision, how fast was the car initially traveling?

A) 14 m/s

B) 7 m/s

C) 28 m/s

D) 11 m/s

A) 14 m/s

Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.

A) 11 m/s at 14° with respect to the original direction of the lighter car

B) 16 m/s at 76° with respect to the original direction of the lighter car

C) 11 m/s at 76° with respect to the original direction of the lighter car

D) 16 m/s at 14° with respect to the original direction of the lighter car

C) 11 m/s at 76° with respect to the original direction of the lighter car

A 2.0-kg mass moving at 5.0 m/s suddenly collides head-on with a
3.0-kg mass at rest. If the collision is *perfectly inelastic*,
what is the speed of the masses just after the collision?

A) 10 m/s

B) 2.5 m/s

C) 2.0 m/s

D) 0 m/s, since the collision is inelastic

C) 2.0 m/s

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the speed of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision.

A) 0.00 m/s

B) 3.0 m/s

C) 4.0 m/s

D) 5.0 m/s

E) 6.0 m/s

D) 5.0 m/s

A fire hose is turned on the door of a burning building in order to knock the door down. This requires a force of 1000 N. If the hose delivers 40 kg of water per second, what is the minimum velocity of the stream needed to knock down the door, assuming the water doesn't bounce back?

A) 15 m/s

B) 20 m/s

C) 25 m/s

D) 30 m/s

C) 25 m/s

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the momentum of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision.

A) 0.00 kg ∙ m/s

B) 1200 kg ∙ m/s

C) 2000 kg ∙ m/s

D) 7200 kg ∙ m/s

E) 6000 kg ∙ m/s

E) 6000 kg ∙ m/s

A 1200-kg car moving at suddenly collides with a stationary car of mass If the two vehicles lock together, what is their combined velocity immediately after the collision?

A) 6.9 m/s

B) 8.6 m/s

C) 12.1 m/s

D) 5.5 m/s

A) 6.9 m/s

A block of mass *m* = 5.6 kg, moving on a frictionless surface
with a velocity of to the right, collides with a block of mass
*M* at rest, as shown in the figure. After the collision, the
5.6-kg block recoils with a velocity of to the left. If the blocks are
in contact for 0.20 s, what is the magnitude of the average force on
the 5.6-kg block, while the two blocks are in contact?

A) 202 N

B) 192 N

C) 182 N

D) 0 N

E) 0 N

A) 202 N

A batter hits a foul ball. The 0.14-kg baseball that was approaching him at 40 m/s leaves the bat at 30 m/s in a direction perpendicular to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the baseball?

A) 9.8 N ∙ s

B) 1.4 N ∙ s

C) 3.5 N ∙ s

D) 5.6 N ∙ s

E) 7.0 N ∙ s

E) 7.0 N ∙ s

A 0.140-kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the ground, and it rebounds with an upward speed of 1.00 m/s. The ball is in contact with the ground for 0.0140 s. What is the average force exerted by the ground on the ball during the time of contact?

A) 2.00 N upwards

B) 2.00 N downwards

C) 22.0 N upwards

D) 22.0 N downwards

E) 0.00 N

C) 22.0 N upwards

A very small 51-g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for 0.50 ms. The ball rebounds elastically and returns to its original height. The total time interval for a round trip is 3.00 s. What is the magnitude of the average force exerted on the ball by the plate during contact with the plate?

A) 3000 N

B) 1500 N

C) 2490 N

D) 2000 N

E) 3500 N

A) 3000 N

A block of mass *m* = 34 kg and speed *V* is behind a
block of mass *M* = 81 kg and speed of as shown in the figure.
The surface is frictionless and the blocks collide and couple. After
the collision, the blocks have a common speed of What is the magnitude
of the impulse on the 34-kg block due to the collision?

A) 32 N ∙ s

B) 14 N ∙ s

C) 41 N ∙ s

D) 57 N ∙ s

E) 73 N ∙ s

A) 32 N ∙ s

A steady horizontal force lasting for 2.1 s gives a 1.25 kg object an acceleration of 3.2 m/s2 on a frictionless table. What impulse does this force give to the object?

A) 26 kg ∙ m/s

B) 11 kg ∙ m/s

C) 8.4 kg ∙ m/s

D) 2.6 kg ∙ m/s

C) 8.4 kg ∙ m/s

A 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of If the clay comes to a stop in what is the average horizontal force on the clay due to the wall?

A) 42 N

B) 26 N

C) 35 N

D) 51 N

A) 42 N

A golf ball of mass 0.050 kg is at rest on the tee. Just after being struck, it has a velocity of 102 m/s. If the club and ball were in contact for what is the average force exerted on the ball by the club?

A) 6.3 kN

B) 7.1 kN

C) 5.5 kN

D) 4.9 kN

A) 6.3 kN

A 0.140 kg baseball is thrown horizontally with a velocity of 28.9 m/s. It is struck with a constant horizontal force that lasts for 1.85 ms, which results in a velocity of 37.0 m/s in the opposite direction. What was the magnitude of the horizontal force?

A) 0.613 kN

B) 2.19 kN

C) 2.80 kN

D) 4.99 kN

D) 4.99 kN

A girl of mass 55 kg throws a ball of mass 0.80 kg against a wall. The ball strikes the wall horizontally with a speed of and it bounces back with this same speed. The ball is in contact with the wall What is the magnitude of the average force exerted on the wall by the ball?

A) 800 N

B) 400 N

C) 55,000 N

D) 27,500 N

E) 13,750 N

A) 800 N

Calculate the impulse due to a force of that lasts for

A) 6.3 kg∙ m/s

B) 5.0 kg∙ m/s

C) 5.7 kg∙ m/s

D) 6.9 kg∙ m/s

A) 6.3 kg∙ m/s

A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball just as it leaves the tee?

A) 30 m/s

B) 35 m/s

C) 40 m/s

D) 45 m/s

E) 50 m/s

C) 40 m/s

A super dart of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30° with the plane of the plate, as shown in the figure. It bounces off the plate at the same angle but at a speed of 320 m/s. What is the magnitude of the impulse that the plate gives to the bullet?

A) 0.52 N ∙ s

B) 4.3 N ∙ s

C) 300 N ∙ s

D) 6.7 N ∙ s

E) 0.30 N ∙ s

D) 6.7 N ∙ s

A forklift pushes a 100-kg crate, starting from rest, with a
horizontal force of magnitude *F*. The graph in the figure
shows the *x *component of this force as a function of time.
What is the instantaneous velocity of the crate at time *t* =
10 s?

A) 25 cm/s

B) 0.00 cm/s

C) 75 cm/s

D) -25 cm/s

E) -75 cm/s

E) -75 cm/s

A 0.140-kg baseball is thrown with a velocity of It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original velocity. How long were the bat and ball in contact?

A) 1.79 *×* 10-3s

B) 1.28 *×* 10-2s

C) 3.07 *×* 10-2s

D) 4.30 *×* 10-3s

A) 1.79 *×* 10-3s

The graph in the figure shows the *x* component *F* of
the net force that acts for 10 s on a 100-kg crate. What is the change
in the momentum of the crate during the 10 s that this force acts?

A) -100 kg ∙ m/s

B) -25 kg ∙ m/s

C) 75 kg ∙ m/s

D) -75 kg ∙ m/s

E) 25 kg ∙ m/s

D) -75 kg ∙ m/s

A 14-cm diameter champagne bottle rests on its side on top of a frictionless horizontal table. Suddenly, the cork pops and the bottle slides backward, covering a distance of in If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position that the cork will land on the table. Neglect air resistance and assume that the cork is very small compared to the bottle.

A) 3000 cm

B) 60 m

C) 85 m

D) 8.5 cm

A) 3000 cm

Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship?

A) 1000 s

B) 750 s

C) 500 s

D) 250 s

E) 2.50 min

C) 500 s

Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved 12 m?

A) 16 m

B) 9.0 m

C) 21 m

D) 7.0 m

E) 12 m

B) 9.0 m

Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m?

A) 9.0 m

B) 16 m

C) 21 m

D) 24 m

E) 28 m

E) 28 m

In a police ballistics test, a 10.0-g bullet moving at 300 m/s is fired into a 1.00-kg block at rest. The bullet goes through the block almost instantaneously and emerges with 50.0% of its original speed. What is the speed of the block just after the bullet emerges?

A) 1.50 m/s

B) 2.97 m/s

C) 3.00 m/s

D) 273 m/s

A) 1.50 m/s

A dinner plate falls vertically to the floor and breaks up into three
pieces, which slide horizontally along the floor. Immediately after
the impact, a 320-g piece moves along the +*x*-axis with a
speed of 2.00 m/s and a 355-g piece moves along the +*y*-axis
with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what
direction relative to the +*x-*axis does the third piece move?

A) 216.9° from the +*x*-axis

B) 219.8° from the +*x*-axis

C) 36.9° from the +*x*-axis

D) 39.9° from the +*x*-axis

E) 39.8° from the +*x*-axis

B) 219.8° from the +*x*-axis