Planet X has the same mass as the Earth, but 1/2 the radius.

(Planet X is more dense than Earth). What is the acceleration of

gravity on Planet X?

A) g (same as Earth)

B) 2g

C) 4g

D) 8g

E) None of these.

Two satellites, A and B, are in circular orbit around the earth. The

distance of satellite B from the center of the Earth is twice that of

satellite A. What is the ratio of the magnitudes of the accelerations of

A to B?

.... A) 1 B) 2 C) 4

D) 1/2 E) 1/4

a

a

A

B

=D) 1/2 E) 1/4aB

A

B

Two satellites, A and B, are in circular orbit around the earth. The

distance of satellite B from the center of the Earth is twice that of

satellite A. What is the ratio of the magnitudes of the speeds ( |v| )

of A to B?

.... A) B) C) 1Av

v=

12

2

D) 1/2 E) 2Bv

A

B

Does escape velocity depend on launch angle? That is, if a projectile is given an

initial speed vo, is it more likely to escape an (airless) planet, if fired straight up

than if fired at an angle?

A) Yes B) No A) Yes B) No

Suppose a projectile is fired straight upward from the surface of an airless

planet of radius R with the escape velocity vesc (meaning the projectile

will just barely escape the planet's gravity -- it will assymtotically approach

infinite distance and zero speed.) What is the projectile's speed when it is

a distance 4R from the planet's center (3R from the surface).

A) 1/2 vesc B) 1/4 vesc

C) 1/9 vesc D) 1/3 vesc

E) None of these is correct.E) None of these is correct.

(Ignore the gravity of the Sun and other astronomical bodies.)

A spring-loaded dart gun shoots a dart straight up into the air, and the

dart reaches a maximum height of 24 m. The same dart is shot straight

up a second time from the same gun, but this time the spring is

compressed only half as far before firing. How far up does the dart go

this time, neglecting friction and assuming an ideal spring?

A) 48m B) 24m C) 12m

D) 6m E) 3m

A block of mass m with initial speed v slides up a frictionless ramp of

height h inclined at an angle θ as shown. Assume no friction

hθvm

True A or False B:

Whether the block makes it to the top of the ramp depends on the

mass of block and on the angle θ.

A block of mass m with initial speed v slides up a frictionless ramp of

height h inclined at an angle θ as shown.

hθvm

Suppose now that there is friction between the block and the ramp

surface.

(A) True or (B) False :

Whether the block makes it to the top of the ramp depends both on

the mass of block and on the angle θ.

A hockey puck slides without friction along a frozen lake toward an ice ramp

and plateau as shown. The speed of the puck is 4m/s and the height of the

plateau is 1m. Will the puck make it all the way up the ramp?

h = 1m v = 4m/s

A. Yes

B. No

C. impossible to determine without knowing the mass of the

puck.

A mass slides down a frictionless ramp of height h and hits a carpet with

kinetic friction coefficient µK = 1.0. Its initial speed is zero. How far does

the mass slide along the carpet?

h h

A) h B) Less than h C) more than h

A block initially at rest is allowed to slide down a frictionless ramp and

attains a speed v at the bottom. To achieve a speed 2v at the bottom,

how many times as high must the new ramp be?

A.

B. 2

C. 3

D. 4

E. None of these

2 14≅ .

E. None of these

A mass m is at the end of light (massless) rod of length R, the other end of

which has a frictionless pivot so the rod can swing in a vertical plane. The rod

is initially horizontal and the mass is pushed down with an initial speed vo .

What initial kinetic energy is required for the mass to pivot 270o to the vertical

position?

=2omv

2

1

R m

vo

=omv2

A. mgR

B. mg(2R)

C. mg(3R)

D. None of these

A planet in elliptical orbit around a star moves from the point in its

orbit furthest from the star (A) to the closest point (P). The work

done by the force of gravity during this movement is:

A) zero B) Positive C) Negative.

A P

A P

The planet executes one complete orbit starting from point A and

returning to A. The work done by the force of gravity during this

orbit is:

A) zero B) Positive

C) Negative.

A pendulum is launched in two different ways. During both launches, the

bob is given an initial speed of 3.0 m/s and the same initial angle from the

vertical. On launch 1, the speed is upwards, on launch 2, the speed is

downwards.

1

2

Which launch will cause the pendulum to swing the largest angle from

the equilibrium position on the left side?

A: Launch 1 B: Launch 2

C: Both launches give the same maximum displacement.

An Atwood's machine is a pulley with two masses connected by a string as

shown. The mass of object A, mA , is twice the mass of object B, mB. The

tension T in the string on the left, above mass A, is...

A. T = mA g

B. T = m g

A

B

A

B. T = mB g

C. Neither of these.

In the 1600's, Otto Van Güricke, a physicist in Magdeburg, fitted two hollow

bronze hemispheres together and removed the air from the resulting sphere

with a pump. Two eight-horse teams could not pull the spheres apart, even

though the hemispheres fell apart when air was re-admitted. Suppose von

Güricke had tied both teams of horses to one side and bolted the other side to

a heavy tree trunk. In this case the tension in the rope would be...

A) twice B) exactly the same as

C) half what it was before.C) half what it was before.

Sandy and Fred are having a tug-of-war. So far, no one is winning.

�FSQ1: What is the direction of the force of friction on Sandy's feet

Sandy Fred

A) Right B) Left→ ←

Q2: How large is the force of friction on Sandy's feet compared to

the force of friction on Fred's feet?

�FS�

FF

� �F FS F>

� �F FS F=

� �F FS F<

A.

B.

C.

A moving van collides with a sports car in a high-speed head-on collision.

During the impact, the truck exerts a force Ftruck on the car and the

car exerts a force Fcar on the truck. Which of the following statements

about these forces is true)about these forces is true)

A) Ftruck = Fcar (The force exerted by the truck on the car is the same size

as the force exerted by the car on the truck)

B) Ftruck > Fcar

C) Ftruck < Fcar

At time t=0, a satellite in circular orbit about the Earth is directly over

Denver, 300 miles above the city, and traveling eastward at 16,000

mph. At the same time, a rock is released from rest 300 miles above

the city, very near the satellite.

rock satellite

Denver

True or False: at t=0+, the accelerations of the rock and

the satellite are identical in magnitude and direction.

A) true B) False

A satellite is in circular orbit around a planet that has a very

tenuous atmosphere extending up to the altitude of the satellite.

Due to atmospheric drag, the speed of the satellite…

A) increases B) decreases

C) remains constant C) remains constant

3

2

r

TKepler's third law states that the ratio is a constant for

all the planets. The period T of the Earth is 1 year. An astronomical unit

(1 A.U.) is defined as the mean distance from the Earth to the Sun,

therefore the mean Earth-Sun distance is 1A.U.

Consider an asteroid in circular orbit around the Sun with radius r = 2A.U. Consider an asteroid in circular orbit around the Sun with radius r = 2A.U.

The period of the asteroid is..

A): 2 years. B) 3 years C) 23/2 ≅ 2.83 years.

D) 22/3 ≅ 1.59 years E) None of these.

A rock is released from rest at a point in space far from Earth, beyond the

orbit of the Moon. The rock falls toward the Earth and crosses the orbit of

the Moon. When the rock is the same distance from the Earth as the Moon,

the acceleration of the rock is ..

(Ignore the gravitational force between the rock and the Moon.)

A) greater B) smaller

C) the same as the acceleration of the Moon.

Earth

Moon

rock

Suppose the Earth had no atmosphere and a projectile was fired from

a mountain top with sufficient speed to put it in circular orbit.

The magnitude of the acceleration of the projectile while in orbit

would be

A. much less than g (because it doesn't fall to the ground)

B. much greater than g

C. approximately g

D. Impossible to tell.D. Impossible to tell.

The "multiflash photograph" below shows a ball rolling along a

surface. The camera flashed once a second, and the time is

shown above each image. Which

graph below best represents the graph below best represents the

ball's velocity as a function of time?

An object's acceleration vs. time is:

Which graph best represents the object's velocity vs. time?

A

)

A) B)

C) D)

E)

A mass m accelerates downward along a frictionless inclined plane. The

magnitudes of the forces on the free-body diagram have not been drawn

carefully, but the directions of the forces are correct.

N

a

mg

Which statement below must be true?

A. mg > N

B. N > mg

C. N=mg

A) N mgsin m a− θ =

N

y

A student chooses a tilted coordinate system as shown, and then

proceeds to write down Newton's 2nd Law in the form .

What is the correct equation for the y-direction ?

x x y yF m a , F m a= =∑ ∑y yF m a=∑

B)

C)

D)

E)

mgsin m aθ =

N mg m a+ =

N mg cos m a− θ =

N mg cos 0− θ = θ

θ mg

N

x

a

A rider in a "barrel of fun" finds herself stuck with her back to the wall.

Which diagram correctly shows the forces acting on her?

Pink Blue Green Purple Yellow A) B) C) D) E)

Conical pendulum

At the instant shown, which free-body diagram best

indicates the forces acting on the pendulum?

Which is larger ? A) the weight mg

B) the tension T

A bucket containing a brick is swung in a circle at constant speed in a vertical

plane as shown. The bucket is swung fast enough that the brick does not fall

out.

N R

T

When the bucket is at the right,

position R, which of the following is a

correct free body diagram on the brick?

N R

B

D) None of these

A) B) C)

A bucket containing a brick is swung in a circle at constant speed in a vertical

plane as shown. The bucket is swung fast enough that the brick does not fall

out.

N R

T

When the bucket is at the top, position

T, which of the following is a correct

free body diagram for the brick?

N R

B

A) B) C)

D) None of these

A bucket containing a brick is swung in a circle at constant speed in a vertical

plane as shown. The bucket is swung fast enough that the brick does not fall

out.

N R

T

When the bucket is at the bottom,

position B, which of the following is a

correct free body diagram for the

brick?N R

B

A) B) C)

D) None of these

A bucket containing a brick is swung in a circle at constant speed in a vertical

plane as shown. The bucket is swung fast enough that the brick does not fall

out.

N R

T Which of the following are Newton III force pairs?

A. Weight force on the brick, and the normal force

on the brick due to the bucket

N R

B

B. Weight force on the brick and the tension in the

rope

C. Mv2/r on the brick and the tension in the rope

D. Force on the brick by the rope and the normal

force by the bucket on the brick

E. None of these

A person swings on a swing. When the person sits still, the swing

oscillates back and forth at its natural frequency.

If, instead, the person stands on the swing,

the natural frequency of the swing is..

A: greater.

B: the same.B: the same.

C: smaller.

Consider a person standing in an elevator that is moving upward at an

increasing speed. The magnitude of the upward normal force, N,

exerted by the elevator floor on the person's feet is

A. larger than

B. the same as

C. smaller than

the magnitude of the downward weight, W, of the person.

speed v

A car is sitting on the surface of the Earth and both the car

and the Earth are at rest. (Pretend the Earth is not rotating or

revolving around the Sun.) The car accelerates to a final

velocity.

After the car reaches its final velocity, the magnitude of the

Earth's momentum is __________ the magnitude of the car's

momentum.momentum.

A) more than B) the same as C) less than

D) cannot answer the question because the answer depends on the

interaction between the Earth and the car.

Suppose the entire population of Earth gathers in one location and, at a

pre-arranged signal, everyone jumps up. About a second later, 6 billion

people land back on the ground. After the people have landed, the

Earth's momentum is..

A. the same as it was before the people jumped.

B. different than it was before the people jumped.

C. impossible to know whether the Earth's momentum changed/don't C. impossible to know whether the Earth's momentum changed/don't

know.

After the 6 billion people have passed the apex of their jump and are on

the way down, the velocity of the Earth is..

A. away from the people

B. toward the people

C. zero

Two light (massless) rods, labeled A and B, each are connected to the

ceiling by a frictionless pivot. Rod A has length L and has a mass m at the

end of the rod. Rod B has length L/2 and has a mass 2m at its end. Both

rods are released from rest in a horizontal position.

L/2 A

B

L

L/2

m

2m

A

Which one experiences the larger torque?

A) A B) B C) Both have the same size τ.

Two light (massless) rods, labeled A and B, each are connected to the

ceiling by a frictionless pivot. Rod A has length L and has a mass m at the

end of the rod. Rod B has length L/2 and has a mass 2m at its end. Both

rods are released from rest in a horizontal position.

L/2 A

B

L

L/2

m

2m

A

Which one falls to the vertical position fastest?

A) A B) B C) Both fall at the same rate

ατ

=I

Hint

The period of a physical pendulum is .

Compare the periods of two physical pendula. One is a solid disk of mass m,

radius R, supported at the edge. The other is a hoop also of mass m, radius

R, supported at the edge.

TI

mgL= 2π

pivot pivot

C.M. C.M.

Disk Hoop

Which has the longer period?

A) Disk B) Hoop C) The periods are the same.

The period of a physical pendulum is .

Compare the periods of two physical pendula. One is a solid disk of mass m,

radius R, supported at the edge. The other is a hoop also of mass m, radius

R, supported at the edge.

TI

mgL= 2π

pivot pivot

C.M. C.M.

Disk Hoop

On the moon, is the period different than on the Earth?

A) longer on Moon B) shorter

The period of a physical pendulum is .

Compare the periods of two physical pendula. One is a solid disk of mass m,

radius R, supported at the edge. The other is a hoop also of mass m, radius

R, supported at the edge.

TI

mgL= 2π

pivot pivot

C.M. C.M.

Disk Hoop

What happens to the period T of the hoop physical pendulum, when the

mass is doubled? (Careful! What happens to I?)

A) Tnew = Told B) Tnew = (Told)/2

C) T Tnew old= / 2

A planet in elliptical orbit about the Sun is in the position shown.

S A B

How does the magnitudes of the angular momentum of the planet

Lplanet (with the origin at the Sun) at positions A and B compare?

A) LA=LB

B) LA>LB

C) LA<LB

A planet is in elliptical orbit around the Sun. The zero of potential energy U is

chosen at r = ∞, so

U rGMm

r( ) = −

How does the magnitude of U (= -U) compare to the KE?

A) -U > KE B) -U < KE C) -U=KE

D) depends on the position in the orbit.

A planet in elliptical orbit about the Sun is in the position shown.

S

planet

x

y

z

With the origin located at the Sun, the vector torque on the planet..

A) is zero. B) points along +z.

C) is in the x-y plane. D) None of these.

A planet in elliptical orbit about the Sun is in the position shown.

S A B

How does the magnitudes of the angular momentum of the planet

Lplanet (with the origin at the Sun) at positions A and B compare?

A) LA=LB

B) LA>LB

C) LA<LB

The gravitational potential energy of a rock near a star is shown in the

diagram. When the rock is at the position shown, it has a kinetic

energy of 25MJ. Will the rock escape to infinity or is it bound in orbit

about the star?

A) Escape B) in bound orbit

C) impossible to tell

U(r) r

-10MJ

0

-20MJ

-40MJ

A new "constant force spring" is invented which has the remarkable

property that the force exerted by the spring is independent of the stretch

of the spring, Fspr = -q, where q is a constant. What is the potential energy

contained in this spring when it is stretched a length x.

A) (1/2)qx2 B) q x C) q

D) None of these. D) None of these.

A block is pushed up an incline with a constant force

L

θ

What is the work done by the force F?

A) FL B) FLsin(θ) C) FLcos(θ) D) 0

F

A block is pushed up an incline with a constant force

L

θ

What is the magnitude of the work done by gravity W=mg?

A) WL B) WLsin(θ) C) WLcos(θ) D) 0

F

A block is pushed up an incline with a constant force

L

θ

If the speed of the block is constant, what is the magnitude of the net work

done?

A) FL B) WLsin(θ) C) FL-WLsin(θ) D) 0

F

A door is pushed on by two forces, a smaller force at the door knob and a

larger force nearer the hinge as shown. The door does not move.

Big force

Small force.

hinge

x

y

Big forcex

The force exerted on the door by the hinge...

A) points → (along +x)

B) points ← (along –x)

C) points ↓ (along -y)

D) points (lower right, in diagram)

E) points (upper right, in diagram)ր

Three forces labeled A, B, C are applied to a rod which pivots on an

axis thru its center

[ ] 0 0cos(45 ) sin(45 ) 1/ 2 1/1.414= = =

2F

o

L/2

L C

F

F

45o

L/4 A

B

Which force causes the largest magnitude torque?

A) A B) B C) C

D) two or more forces tie for largest size torque.

A mass M is placed on a very light board supported at the ends, as

shown. The free-body diagram shows directions of the forces, but not

their correct relative sizes.

(2/3)L L/3

M

Mg

FL FR

(2/3)L L/3 Mg

What is the ratio ?

A) 2/3 B) 1/3 C) 1/2 D) 2

E) Some other number.

F

F

R

L

A uniform rod of length L, mass M, with one end on the ground is

released from rest at an angle θ from the horizontal. It falls over,

rotating about the bottom end. Immediately after the rod is released,

the upper end

θθ

has angular velocity ω =___ and angular acceleration α = ____

A: zero, zero B: not zero, not zero.

C: zero, not zero D: not zero, zero

A uniform rod of length L, mass M, with one end on the ground is

released from rest at an angle θ from the horizontal. It falls over,

rotating about the bottom end. Immediately after the rod is released,

the upper end

θθ

has tangential acceleration at ____

and has radial acceleration ar ______

A: zero, zero B: not zero, not zero.

C: zero, not zero D: not zero, zero

A small wheel and a large wheel are connected by a belt. The small

wheel is turned at a constant angular velocity ωs. How does the

magnitude of the angular velocity of the large wheel ωL compare to

that of the small wheel?

ωs

ωLωs

A) ωs = ωL B) ωs < ωL C) ωs > ωL

A small wheel and a large wheel are connected by a belt. The small

wheel is turned at a constant angular velocity ωs.

ωs

ωLωs

There is a bug S on the rim of the small wheel and another bug L on the

rim of the large wheel. How do their speeds compare?

A) S = L B) S > L C) S < L

A horizontal wheel of radius R is spinning freely with constant

angular velocity about a fixed axis.

At what point on the wheel is the magnitude of the linear acceleration, a, the

largest?

A: near the center B: along the rim

C: somewhere roughly midway between the center and the rim.

D: Nowhere, a=0 everywhere on the wheel

A disk is spinning as shown with angular velocity ω. It begins to slow

down.

�α

While it is slowing, what is the direction of its vector angular

acceleration

A) ↑ B) ↓C) ← D) →E) Some other direction.

A ladybug is clinging to the rim of a spinning wheel which is

spinning CCW very fast and is slowing down. At the moment

shown, what is the approximate direction of the ladybug's

acceleration?

Pink:

Yellow:

Blue:A) B)

Yellow:

Green:

Purple: None of these.

D)

C) E) None of these

A student in Physics 1110 sees the following CAPA question.

An engine flywheel turns with constant angular speed of 100 rev/min. When

the engine is shut off, friction slows the wheel to rest in 2 hours. What is

the magnitude of the constant angular acceleration of the wheel? Give the

answer in units of rev/min2.

The student writes

ω ω α ω

αω π π

= + =

= = =

o

orev

t

t

f

t

, ,

( )

min.

min

0

2 2 100

120

so

Does the answer come out correctly with the desired units?

A) Yes B) No

A mass m hangs from string wrapped around a pulley of radius R. The pulley

has a moment of inertia I and its pivot is frictionless. Because of gravity the

mass falls and the pulley rotates.

R

The magnitude of the torque on the pulley is..

A) greater than mgR

B) less than mgR

C) equal to mgR

m

C) equal to mgR

(Hint: Is the tension in the string = mg?)

Consider a solid disk with an axis of rotation through the center

(perpendicular to the diagram). The disk has mass M and radius R A

small mass m is placed on the rim of the disk. What is the moment of

inertia of this system?

A. (M+m)R2

B. less than (M+m)R2B. less than (M+m)R2

C. greater than (M+m)R2

A sphere, a hoop, and a cylinder, all with the same mass M and

same radius R, are rolling along, all with the same speed v.

Sphere Hoop Disk

v v v

Which has the most kinetic energy?

A) SphereB) Hoop C) Disk

D) All have the same KE.

A horizontal hoop of mass M and radius R is rotating about a frictionless

pivot with frequency fo. A disk, also of mass M and radius R, is dropped

from rest onto the hoop. The disk sticks to the hoop. What is the final

frequency of the (hoop + disk)?

Ihoop = MR2 Idisk = (1/2)MR2

A: (1/2)fo B: (1/4)fo

C: (2/3)fo D: fo (No change)

E: None of these/don't know.

Two wheels with fixed axles, each have the same mass M, but wheel 2 has

twice the radius of wheel 1. Each is accelerated from rest with a force

applied as shown. Assume that all the mass of the wheels is concentrated in

the rims so that the moment of inertia of each is of the form I = M R2 (hoop

formula). In order to impart identical angular accelerations to both wheels,

how much larger is F2 than F1? Recall that

F1

F2

Iτ = α

R

F1

Wheel 1, radius R, mass M

2

Wheel 2, radius 2R, mass M

2R

A) F2 = F1 B) F2 = 2F1

C) F2 = 4F1 D) F2 = 8F1

E) None of these.

Consider a rod of uniform density with an axis of rotation through its

center and an identical rod with the axis of rotation through one end.

Which has the larger moment of inertia?

C E

axisaxis

A) IC > IE B) IC < IE C) IC = IE

Consider two masses, each of size 2m at the ends of a light rod of

length L with the axis of rotation through the center of the rod. The

rod is doubled in length and the masses are halved. What happens to

I?

A BL/2L/2

mL L m

2m 2mm

L L m

A) IA > IB B) IA < IB C) IA = IB

A mass is hanging from the end of a horizontal bar which pivots about

an axis through it center, but it being held stationary. The bar is released

and begins to rotate. As the bar rotates from horizontal to vertical, the

magnitude of the torque on the bar..

A) increases B) decreases C) remains constant

A mass is hanging from the end of a horizontal bar which pivots about

an axis through it center, but it being held stationary. The bar is released

and begins to rotate.

As the bar rotates from horizontal to vertical, the magnitude of the

angular acceleration α of the bar..

A) increases B) decreases C) remains constant

Three identical wheels are all spinning with the same angular velocity . The total

angular momentum of the 3-wheel system has magnitude L.

�ω

ω ω ω

One of the three wheels is flipped upside-down, while the magnitude of

its angular velocity remains constant.

The new angular momentum of the 3-wheel system has magnitude..

A) L (the same as before) B) (2/3)L C) (1/3)L

D) some other value.

A star is rotating with a period T. Over a period of a million years, its

radius decreases by a factor of 2. What is the new period of the star?

(Hint: )I M Rsphere = 25

2

A)T/2 B) 2T

C) 4T D) T/4

E) None of these.E) None of these.

A disk of mass M and area A and radius R is reshaped into a square of

the same area A (and the same mass M). The edge length L of the

square is related to the radius R of the disk by L2 = πR2.

The moment of inertia I of the square is

A: larger B: smaller

C: the same as

the moment of inertia I of the disk.

Consider a solid disk with an axis of rotation through the center

(perpendicular to the diagram). The disk has mass M and radius R. A small

mass m is placed on the rim of the disk.

Suppose the disk was on a phonograph player, so that it always turned at 33

rpm. As Atom-Ant moves inward, the speed of the mass m

A) increases B) decreases C) remains constant