now by Test Day

plied to a 15-kg object throughout a

:ement

Torque and Rotational Motion

!ct throughout the 8.0-m

Questions 301-315 are easier practice questions designed to allow the student sPecific AP learning objectives and essential knowledge of torque and o review

rotational motion.

301. What happens to the rotational kinetic energy of an object if its rotational

speed is tripled?

(A) The rotational kinetic energy is nine times as much.

(B) The rotational kinetic energy triples. (C) The rotational kinetic energy stays the same.

(D) The rotational kinetic energy is one-third as much.

302. As an ice skater is spinning, she extends her arms away from her body. Assuming the friction on the ice is negligible, her angular velocity , and her angular momentum

(A) Decreases; increases (B) Increases; decreases (C) Decreases; decreases (D) Decreases; remains the same

a velocity of +4.0 m/s (before the s kinetic energy after the work was

le work was done on it.

ring with a spring constant of pression of the spring. 303. At t = 0, a circular disk is initially rotating with a positive angular velocity

of 6 radians per second. The rotation slows down at a uniform rate of 2 radians per second each and every second. What are the signs of the angular velocity, angular acceleration, and net torque at the 4-second clock reading?

Net torque Angular velocity Angular Acceleration

Positive

Negative

Negative

Positive

Positive

Negative

Negative

Negative

(A) Positive

(B) Negative

(C) Positive

(D) Negative

97

98 ) 500 AP Physics 1 Questions to Know by Test Day

304. A crane is used to pick up a 50.0-m-long steel beam to place in a building The beam is uniform and horizontal, but the crane cable is placed 2.0 off the center of the beam. How much vertical force must be placed on the guide rope to keep the beam level? The beam has a mass per meter of length is 5.0 kg/m, and the guide rope is placed on the end of the shorter side of the beam.

(A) 220 N (B) 50N (C) 22N (D) 5N

305. When a skater performs a spin on ice with his arms outstretched, what happens when he brings his arms close to his body?

(A) His angular acceleration decreases because his rotational inertia decreases.

(B) His angular acceleration increases because his rotational inertia decreases.

(C) His angular velocity decreases because his rotational inertia decreases. (D) His angular velocity increases because his rotational inertia decreases.

306. A dry ice puck tethered to a string revolves in a horizontal circle on a smooth surface. If the string breaks, what happens to the angular momentum of the puck relative to center of its initial orbit? Assume friction and air drag are negligible.

(A) It increases. (B) It decreases. (C) It immediately increases when the string breaks, then decreases. (D) It remains constant.

307. The rotational inertia of a thin-walled cylinder around its central axis is given by mR2. What expression best represents the angular momentum of this cylinder if it spins about the central axis at a rate of 12 revolutions per second?

(A) (24 7)mR2 (B) (12 7c)mR2

(C) 12mR2

(D) 1 imR2 12

OE

309

310

311

312

Torque and Rotational Motion 99 (now by Test Day

308. -long steel beam to place in a build in 1, but the crane cable is placed 2.0 in ich vertical force must be placed on el? The beam has a mass per meter of pe is placed on the end of the shorter

The Moon orbits the Earth once 385,000 km. What is the orbital

second?

(A) 0.163 m/s

(B) 27.3 m/s (C) 163 m/s (D) 1,030 m/s

every 27.3 days with an orbital radius of speed of the Moon in units of meters per

volves in a horizontal circle on , what happens to the angular nter of its initial orbit? Assume

ie string breaks, then decreases.

cylinder around its central axis is epresents the angular momentum of -al axis at a rate of 12 revolutions per

309. A boy and girl are on a rotating merry-go-round. The girl is on the outer edge, while the boy is halfway between the center and the girl. How does

the angular speed of the girl compare to that of the boy?

(A) The girl's rotational speed is four times as much.

(B) The girl's rotational speed is twice as much.

(C) The girl's rotational speed is the same.

(D) The girl's rotational speed is half as much.

310. A boy and girl are still on the rotating merry-go-round. The girl is on the outer edge, while the boy is halfway between the center and the girl. How

does the linear speed of the girl compare to that of the boy?

(A) The girl's linear speed is four times as much.

(B) The girl's linear speed is twice as much.

(C) The girl's linear speed is the same. (D) 'The girl's linear speed is half as much.

311. A propeller, initially at rest, rotates about its midpoint with an angular acceleration of 12 radians/sec2. How much time will it take to rotate

through a 90.0° angle?

(A) 0.51 s (B) 0.72s (C) 1.2s (D) 3.9 s

312. A disk, initially rotating at +11 rad/s, slows down at a constant rate of

1.5 rad/s2. What is the angular displacement of the disk through an

elapsed time of 6.0 s of time?

(A) 9.0 rad (B) 27 rad (C) 39 rad (D) 66 rad

e with his arms outstretched, what ■se to his body?

ses because his rotational inertia

,es because his rotational inertia

ecause his rotational inertia decreases. cause his rotational inertia decreases.

Que

At a fire 1 25 ci

one e

targei

318.

100 ) 500 AP Physics 1 Questions to Know by Test Day

313. A car tire is initially spinning with an angular speed of 150 radians per second. As the brakes are applied, the tire slows down at a rate of 25 rad/s2. How much time does it take the car to stop?

(A) 2.0 s (B) 2.5 s (C) 3.0 s (D) 6.0 s

314. Two children make a seesaw out of a 5.0-m wooden plank. They balance it on a fulcrum located 2.0 m from the left end. The 42.0-kg child sits at the end of the plank on the left side. What distance (measured from the fulcrum) can the 35-kg child sit on the right side of the plank to keep it balanced?

(A) 1.0 m (B) 1.5m (C) 2.0 m (D) 2.4 m

315. An object, initially rotating with an angular speed of +15 rad/s, is subjected to a torque of +55 Nm that accelerates it constantly at +5.0 rad/s2. What is the rotational inertia of the object?

(A) 3.0 kg- m2 (B) 3.5 kg- m2 (C) 5.5 kg • m2 (D) 11 kg- m2

Questions 316-350 are higher-level, AP-style questions designed to test enduring understanding of AP content.

IV.

31'7

316. The figure above shows four identically-shaped discs, each with a fixed axis of rotation at their centers. Disk IV has twice the rotational inertia of disks I, II & III. The disks are subjected to a variety of forces as shown. Rank the magnitude of the angular acceleration of the disks.

(A) III > II = IV > I (B) I = II = III = IV (C) II =IV > I = III (D) II > I = III = IV

now by Test Day Torque and Rotational Motion ( 101

angular speed of 150 radians per tire slows down at a rate of e the car to stop?

.0-m wooden plank. They balance left end. The 42.0-kg child sits at

That distance (measured from the right side of the plank to keep it

317. As shown in the figure above, a wheel (mass m) starts at rest at the top of an incline (height h) and rolls without slipping to the bottom of the incline with a speed v. Assuming the effect of air drag is negligible, which of the following is a true statement?

1 (A) mgh> —mv

2

2

(B) mgh —1 mv2 2

(C) mgh = —mv2

2 (D) Additional information is needed to compare these quantities.

ular speed of +15 rad/s, is :celerates it constantly at ia of the object?

luestions designed to test

IV.

Questions 318-319 refer to the following information:

At a carnival, one of the booths has a shooting gallery with spring-loaded guns that fire 12-g suction-cup darts with a muzzle velocity of 2.5 m/s. The 95-g targets are 25 cm tall and hinged at the bottom and may be modeled as a plank pinned at

one end (1 = —1 ML ). Assume the dart is moving horizontally when it hits the 3

target 5 cm from the top edge and that the hinge has negligible friction.

2F 2F

aped discs, each with a fixed axis iice the rotational inertia of disks riety of forces as shown. Rank of the disks.

318. Determine the magnitude of the angular momentum of the dart/ target system immediately after the target is hit if angular momentum is measured relative to the hinge of the target.

(A) 0.0015 kg m2

kg m

• 2

(B) 0.0030

kg M• 2 (C) 0.0060

kg m

• 2

(D) 0.0120

102 500 AP Physics 1 Questions to Know by Test Day

319. What is the angular speed of the dart/target system immediately after the target is hit?

(A) 2.4 rad/s (B) 3.0 rad/s (C) 6.0 rad/s (D) 12.5 rad/s

Pulley: Rotational inertia = I Radius = R

Questions

diagra arid is initi forces are act perpen

•

Li

322. Wha angu

(A) (B) (C) (D)

323. If bot

(A)

320. Taken by itself, a pulley has a rotational inertia land radius R. A string is wrapped around the pulley and a mass M is hung from the end of it as shown in the diagram above. Which of the following is true about the magnitude of the angular acceleration of the pulley?

(A) lal < igR

(B)

(C) 1 MgR=

(D) More information is needed.

321. A door rotates about its hinges with negligible friction. A piece of putty is thrown at the door and sticks above the door handle. Is angular momentum conserved during the collision?

(A) Yes, but only if the door is considered as the system. (B) Yes, it is conserved for the door/putty system. (C) Not necessarily; the angle that the putty strikes the door must be

known. (D) No, because the putty exerts a net torque about the axis of rotation.

(C)

iart/target system immediately after t

ia =

mai inertia land radius R. A string rriass M is hung from the end of it ch of the following is true about the n of the pulley?

Questions 322-323 refer to the following information.

The diagram below shows a top-view of a rod that is free to rotate about its center

and is initially rotating with a positive counterclockwise angular velocity we,. Two forces are applied to the rod that are steady in magnitude and will continue to

act perpendicular to the rod, even after it rotates.

322. What value of the unknown downward force will result in a constant angular velocity of the rod?

(A) F (B) F/2 (C) 2F (D) 4F

to Know by Test Day

323. If both forces in the diagram are equal in magnitude, which of the following graphs best represent the angular velocity verses time?

Torque and Rotational Motion < 103

egligible friction. A piece of putty the door handle. Is angular sion?

lered as the system. , utty system.

putty strikes the door must be

torque about the axis of rotation.

104 > 500 AP Physics 1 Questions to Know by Test Day

324. A body with a rotational inertia 4 kg- m2 accelerates constantly from rest 28. A o with an angular acceleration of 5 rad/s2. How much time does it take to deo obtain a rotational kinetic energy of 800 J? Ho (A) is (A) (B) 2s (B) (C) 4 s (C) (D) 8 s (D)

325. Object 1 has a rotational inertia of 8 kg. m2, and Object 2 has a rotational inertia of 2 kg. m2. If Object 1 is rotating with an angular velocity of 1 rad/s, what angular velocity would give Object 2 the same rotational kinetic energy?

(A) 0.25 rad/s (B) 0.5 rad/s (C) 1.0 rad/s (D) 2 rad/s

326. A disk spins at a rate of 4 rad/sec. Later, mass is added to the disk so that its rotational inertia doubles and it is spun up to a rate of 8 rad/sec. How does the magnitude of the new disk's angular momentum compare to the original disk?

(A) The angular momentum doubles. (B) The angular momentum quadruples. (C) The angular momentum stays the same. (D) The angular momentum is one-half as much.

327. A cylinder has a rotational inertia, I. How much time does it take a torque, T, to increase its angular speed from (01 to (02?

(A) gui2 —

(B) /w2

(C) (h.o2 — /WI )T

(D) 1 2 1 /U)2 /W21

2 2

329. The rot. A p and exp rod

(A)

(B)

(C)

(D)

) Know by Test Day Torque and Rotational Motion < 105

:g. m2 accelerates constantly from rest d/s2. How much time does it take to 1800J?

3 kg- m2, and Object 2 has a rotational rating with an angular velocity of ' give Object 2 the same rotational

328. A car wheel has a rotational inertia of 1.5 kg. m2. A brake is applied, which decreases its rotational velocity from 25 revolutions per second to zero. How much energy is transferred to thermal energy in the braking process?

(A) 470J

(B) 940J

(C) 1,900J (D) 19,000J

4 V Ak Puck: w mass = m

Rod: mass = 4m rotational inertia = / length =

Air Table Top

329. The diagram above shows a top view of a long rod (length = , mass = 4m, rotational inertia = /) that sits at rest on its side on a frictionless air table. A puck (mass = m) initially slides to the left with a speed v, strikes the rod, and bounces back to the right, moving at half its initial speed. Develop expressions for the linear speed ( v,ad ) and rotational speed ( w„d ) of the

rod immediately after the collision. mv

(A) v„d = —v

and w„d = 4 21

3v 3mv (B) v,,,, = — and Lora —

e

4 2/

mv (C) v„,/ —

v and Lo a r =

8 4/

3v 3mv (D) v„d = — and w„d = e

8 4/

ter, mass is added to the disk so that spun up to a rate of 8 rad/sec. How angular momentum compare to the

s. pies. e same. ialf as much.

low much time does it take a torque, )1 to 0)2?

106 ) 500 AP Physics 1 Questions to Know by Test Day

330. A barbell consists of along, uniform rod with the center of 3.0-kg masses attached to each end. The rod is 2.2 m long and has a rotational inertia about its center of mass of 1.5 kg. m2. Calculate the rotational momentum of the barbell when it rotates at 0.50 rad/s about the center of the rod.

(A) 1.1 kg • in2

(B) 2.2 kg • m2

(C) 3.0 kg • m2

3 3.

(D) 4.4

Pivot Pivot

IV.

60° 2F

Pivot

331. Four identical rods shown above experience the forces as shown. Rank the magnitude of the torques about the pivot point on the left end of the rod.

(A) III > I = IV > II (B) II > IV > III > I (C) I III = IV > II (D) III > II > I > IV

332. Starting from rest, a spinning disk accelerates uniformly to a final rotational speed, to, in a period of time, At. What expression best represents the revolutions the disk has turned through during this time?

334. 1

a

Sr

0

(A)

(B)

(C)

(D)

wAt

27c

wAt

47 wAt2

2

At

F/2

Pivot

Know by Test Day Torque and Rotational Motion < 107

333. A baton of length L rotates with a constant angular speed, w, measured in radians per second. What is the period of the baton's rotation?

27L (A)

rod with the center of 3.0-kg masses m long and has a rotational inertia a. Calculate the rotational momentu rad/s about the center of the rod.

IF

334. A sphere (mass = m, radius = R, moment of inertia = —2 mR

2) is sliding on

5 a frictionless table with linear speed v and does not rotate. An identical sphere is spinning on the same table (not sliding) about its center with an angular

velocity, B. What is the ratio between the kinetic energy of the sliding sphere and the kinetic energy of the rotating sphere?

(A) 5v2

2R2w2

f.nce the forces as shown. Rank the yt point on the left end of the rod.

Tates uniformly to a final At. What expression best rned through during this time?

108 500 AP Physics 1 Questions to Know by Test Day

Questions 335-336 refer to the following diagram:

A comet orbits the Sun in a periodic elliptical orbit as shown below:

A

335. As the comet moves from point A to point B, what happens to the comet's angular momentum about the Sun? (A) increases linearly

(C) decreases (B)

increases proportionally to the square of the distance from the Sun

(D) stays constant

acct. Se beet.

537. A toi scem

338. Whic the a

(A)

(B)

336. What happens to the gravitational potential energy and the kinetic energy, (C) ] respectively, of the comet/sun system as the comet moves from point A to point B?

(D)

(A) increases increases (B) decreases decreases (C) increases decreases 339. aceAfc cl etI (D) decreases increases

(B) / (C) 2 (D) I

340. When two of

(A) 1 (B) 1 (C) 1 (D) 1

(A)

(B)

(C)

(D)

(now by Test Day

liagram:

orbit as shown below:

Torque and Rotational Motion ( 109

mulri-select: For questions 337-341, two of the suggested answers will be correct. Select the two best answers, and record them both on the answer

sheet.

337. A torque is applied about the axis of rotation in which two of the following scenarios?

(A) A force is applied parallel to the lever arm and acts through the axis of rotation.

(B) A force is applied perpendicular to the lever arm and acts through the axis of rotation.

(C) A force is applied perpendicular to the lever arm but not through the axis of rotation.

(D) A force is applied at a 45° angle but not through the axis of rotation.

)int B, what happens to the comet's

re of the distance from the Sun

tial energy and the kinetic energy, the comet moves from point A to

338. Which two methods provide enough information to determine a value for the rotational inertia of a car tire about its center axis?

(A) Apply a known, uniform torque to the tire. Use a rotary motion sensor to graph its angular velocity vs. time.

(B) Measure the tire's mass and radius and use the formula for a solid disk's rotational inertia.

(C) Measure its mass and radius of the tire and let it roll from rest without slipping down an incline of known height. Use a motion detector to measure its speed at the bottom.

(D) Paint a circle on the edge of the tire, mount it on the axle car of a car. Video the car wheel as the car accelerates from rest to a speed of 20 m/s.

339. If a child sits on the edge a rotating merry-go-round, which two accelerations are possible for the child?

(A) Linear acceleration toward the center (B) Angular acceleration (C) Zero acceleration (D) Linear acceleration outward from the center

340. When a solid object rotates with a uniform angular acceleration, which two of the following are true?

(A) The net torque on the object is zero. (B) The net torque on the object is constant and nonzero. (C) The net torque on the object must increase. (D) The object's angular velocity changes at a steady rate.

110 ) 500 AP Physics 1 Questions to Know by Test Day

341. The rotational inertia of a body depends on which two of the following? see resPo

(A) The angular acceleration of the body (B) The distribution of mass in the body (C) The angular velocity of the body shown (D) The axis of rotation of the body f a tree In

ass = 111 umps off

Free response questions 342-346 refer to the following material:

axis of rots

against the

24 N czZ

A 3.0-m-long uniform rod with a mass of 12 kg rotates about an axis through its

center. There are two applied forces as shown in the diagram below that always keep the same angle relative to the rod. The rotational inertia for a rod rotating about its center is given by I ML2.

12

342. Assuming a counterclockwise rotation is positive, calculate the net torque on the rod.

343. Calculate the rotational inertia of the rod.

344. Calculate the angular acceleration of the rod.

345. If the rod accelerates from rest, determine the time it takes the rod to rotate through a 900 angle.

346. How many revolutions does the rod make in 5.0 s?

347. With princi systen round and jt

348. By wl-chang lands? its ma rotatic square

349. Deters outer velocit

350. The ch against Using go-rou the cot symbol the sysi

)y Test Day Torque and Rotational Motion 4: 111

which two of the following?

wing material:

tates about an axis through its e diagram below that always nal inertia for a rod rotating

Free response questions 347-350 refer to the following material:

As shown in the diagram above, a child (mass = m) initially sits at on top of a tree branch at height h above an empty merry-go-round (radius = R, mass 10m) that is initially rotating with an angular velocity wo. The child jumps off the branch and lands on the merry-go-round, a distance RI2 from the

axis of rotation. Later, the child walks to the outer edge and sits, pushing her feet against the ground.

axis

R / 2

Radius = R Mass = 10m

ive, calculate the net torque

ne it takes the rod to rotate

.0 s?

347. Without solving for the angular velocity, state and discuss the main physics principle needed determine the angular velocity of child/merry-go-round system after the child lands and walks to the outer edge of the merry-go-round (and before she pushes her feet against the ground). Also, discuss and justify assumptions which must be made to apply this principle.

348. By what percentage does the angular velocity of the merry-go-round change from before child lands compared to immediately after the child lands? Note: The rotational inertia of a point particle is the product of its mass and the square of the distance from the axis of rotation. The rotational inertia of a solid disk is the product of half its mass and the square of its radius.

349. Determine the system's angular velocity at the instant the child reaches the outer edge of the merry-go-round as a fraction of the post-drop angular velocity of the child/merry-go-round system, W " r rap'

350. The child now sits at the edge of the merry-go-round and pushes her shoes against the pavement with a steady force with a vertical component F. Using the symbol (-JR for the starting angular velocity of the child/merry-go-round system immediately before the force is applied, the symbol 1i for the coefficient of friction between the shoes and the pavement, and other symbols provided in the figure, develop an expression for the time it takes the system to stop rotating.