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AP Physies I Rotatio血aI Motion Review

Mu班ple Cho宣ce

肱,nt狗′ the letter Qfthe choice /hat best conやletes Jhe statement or answer部he qc/eStion.

1. Which ofthe fo11owing quantities measures the abildy ofa force to rotate or accelerate an object around an

axis?

a. axis ofrotation c. momentarm

b. 1everam d. torque

2. To wam up before a game, a baseball pitcher tosses a O.15 kg ball by rotating his foream, Which is O.32 m in

length’tO aCCelerate the ball. The ba11 starts at rest and is throWn at a SPeed of 12 m/s in O.40 s. While the ba11

is in血e pitcher’s hand, What torque is applied to血e ball to produce the angular acceleration?

a. 1.1N●m C.　7.2N●m

b. 11N●m d. 1.4N●m

3. A bucket創Ied with water has a mass of23 kg and is a請ached to a rope that is wound around a ey血der with

a radius ofO"050 m at the top ofa well. What torque does the weight ofthe water and bucket produce on the

Cylinder? (g = 9.81 m/s2.)

a.　34N●m

b. 17N●m

C. 11N'm

d.　23N●m

。皿標4. A unifom horizontal bean wi血a length of6.O m and aweight of 120 N is attached at one end to a wall by a

Pm COmeCtion so that the beam can rotate. The opposite end ofthe beam is supported by a cable attached to

the wall above the pin. The cable makes an angle of60.OO with the beam. What is the tension in the cable

needed to maintain the beam in equilibrium?

a.　35N c.　6.0×101N

b.　69N d. 120N

5. A child with a weight of4.50 × 102 N sits on a seesaw O.60 m from the axis ofrotation. How far from the

axis ofrotation on the other side should a child with a weight of6.00 × 102 N sit so the seesaw will remain

balanced?

a.　0.30m

b.　0.40m

c.　0.45m

d.　0.50m

Na血e: ID: A

6・ Which ofthe following statements is correct?

a. With a net positive torque, the angular acceleration ofan object is cIockwise.

b. With a net positive torque, the angular acceleration ofan o切ect is countercIockwise.

C. With a net negative torque, the angular acceleration ofan object is countercIockwise.

d・ The net force ofan object is not related to the translational acceleration given to the

O助ect.

7. A grinding wheel with a moment ofinertia of2.O kg●m2 is initially at rest. What angular momentum wi11 the

Wheel have lO.O s after a 2.5 N●m tOrque is applied to it?

25 kgom2/s c. 4'O kg●m2/s

7.5 kg.m2/s d. 0.25 kg●m2/s

ball has a mass of7.O kg, a mOment Ofinertia of2.8 × 10「2 kg.m2, and a radius ofO.10 m. Ifit

rolls down the lane without slipping at an angular speed of4.0 × 101 rad/s, What is its angular momentLm?

a・ 0.80kg.m2/s c. 11 kg●m2/s

b. l.4kg●m2/s d. 1.1kg●m2/s

9・ The moment of ine正a ofa cylinder is O"016 kg●m2. Ifthe angular speed is 15.7 rad/s, What is瓜e angular

momentum of血e cylinder?

a. 0.25kg●m2/s c. 19.2kg●m2/s

b. 12・1 kgem2/s d. 28.6kg.m2/s

10. The total kinetic energy ofa baseba11 thrown with a spiming motion is a function ofwhich ofthe following?

a. the ball’s linear speed only

b・ the ba11’s rotational speed only

C. both the ball’s linear and rotational speeds

d. neither the ball’s linear nor the ball’s rotational speed

l l. A bowling ball has a mass of7.O kg, a mOment Ofinertia of2.8 × 10-2 kg●m2, and a radius ofO.10 m. Ifit

rolls down the lane without slipping at a linear speed of 4.O m/s’what is its total kinetic energy?

a. 45J c. 11J

b. 32J d, 78J

12・ A bucket剛ed with water has a mass of23 kg and is attached to a rope that is wound with a crank around a

O.05 m radius cylinder at the top ofa well. The moment ofinertia ofthe cylinder and crank is O.12 kg●m2.

The bucket and water are first raised to the top ofthe we11 and then released to fall back into the we11. What

is the rotational kinetic energy ofthe cy血der and crank at the instant the bucket is moving at a speed of 7.9

m/s?

a. 2.1×103J c. 7.0×102J

b. 1.5×103J d. 4.0×102J

13. A solid sphere with a mass of4・O kg and a radius ofO.12 m st創rtS from rest atthe top ofa ramp inclined at

15O and rolls to the bottom. The upper end ofthe ramp is l.2 m higher than the lower end. What is the total

kinetic energy ofthe sphere when it reaches the bottom? (Assume that the sphere rolls without slipping and

thatg= 9.81 m/s2,)

a.　70J

b.　47J

c. 18J

d.　8.8J

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14. A disk is intially rotating countercIockwise around a fixed axis with angular speed ①0.

At time t = 0’the two forces shown in the figure above are exerted on the disk. IfcountercIockwise is

POSitive, Which of the following could show the angular velocity ofthe disk as a function oftime?

担事∴∴音脚

〔町

韓a.　a

b. b

C.　C

d.　d

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N租me: Ⅱう: A

15. A child ofmass M is on a rotating circular platfom ofmass 5M that is rotating counterclockwise. Assume

the platfom rotates without friction. Which ofthe following describes an action by血e child that will result

in an increase in the total angular momenturm ofthe chilc-Platfom system?

a. The childmoves towardthe centerofthe c. The childmoves alongacircle

Platfom'　　　　　　　　　　　　　　　　COnCentric with the platfom opposite the

direction of the platfom-s rotation.

b. The child moves away from the center of d. None ofthe actions described will

the platfom.　　　　　　　　　　　　　change the total angular momentum of

the child-Platfrom system.

16. At the top oftwo similar ramps, twO Objects are released from rest. A sphere rolls down one without

Slipping, While a block slides down the other w肌out friction. Which reaches the bottom of its ramp first and

Why?

a. The sphere, because it gains rotational c. The block, because it does not lose

kinetic energy, but血e block does not.　　　mechanical energy due to friction, but the

SPhere does.

b・ The sphere, because it gains mechanical d. The block, because it does not gain

17. ‰

energy due to torque exerted on it, but rotational energy due to friction, but the

the block does not.　　　　　　　　　　　sphere does.

血e top oftwo similar ramps, tWO O助ects are released from rest. A sphere ro11s down one without

Slipping, While a cylinder rolls down the other without slipping. Which reaches the bo請Om Of its ramp first

and why?

a. The sphere, because it gains more c. The cylinder, because it gains more

rotational kinetic energy.　　　　　　　　rOtational kinetic energy.

b. The sphere, because the cylinder gains d. The cylinder, because the sphere gamS

more rotational kinetic energy.　　　　　　more rotational kinetic energy.

1 8. An otlject in mechanical equilibriun must satisfy the following condition(S).

a. Net extemal force must be zero.　　　c. Net extemal torque must be zero.

b. Net extemal torque and force must be d. Net intemal torque and force must be

19. A woman ofmass 55.O kg sits atthe end ofa seesaw ofleng瓜4.00 m that is pivotedわout its middle. Where

Should a man ofmass 75.O kg sit that would result in no net torque?

a. 1.25 mfromthepivot.　　　　　　　c. 1.10from瓜epivot.

b. 1.47mfromthepivot d. .750fromthepivot.

20. A force of4.O N is applied to a door at an angle of60.OO and a distance ofO.30 m from the hinge. What is the

torque produced?

a. 1.ON●m C.　0.87N●m

b. 0.75N●m d. 0.22N●m

21. Suppose a doorknob is placed at the center ofa door. Compared with a door whose knob is Iocated at the

edge, What amount of force must be applied to this door to produce the torque exerted on the other door?

a.　one-halfas much c.　one-fourth asmuch

b. twotimesasmuch d. fourtimesasmuch

22. Ifthe torque required to Ioosen a nut on a wheel has a magnitude of40.O N・m and the force exerted by a

mechanic is 133 N, how far from the nut must the mechanic apply the force?

a.　60.Ocm c.　30.Oc血

b. 15.Ocm d. 1.20m

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Name:

23. At which point in the figure above is the approximate center ofmass?

a・ A c. c

b. B d. D

24・ Which ofthe following is NOT an intrinsic property ofan o寄ect?

a. maSS c. centerofmass

b. moment ofinertia d. center ofgravity

25. Which ofthe fo11owing statements is correct?

a・ The farther the center ofmass ofan (壇eCt is from the axis ofrotation, the less di飾cult it

is to rotate the o巧ect.

b. The farther the center ofmass ofan oqiect is from the axis ofrotation, the sm。11e. th。

O巧eCt’s moment of inertia is.

C. The farther the center ofmass ofan o申yct is from the axi叩frotation,血e greater the

Object’s moment of inertia is.

d. The farther the ∞nter Ofmass ofan o匝ct is from the axis ofrotation, the greater the

Object’s moment ofinertia is, but the less d瓶cult it is to rotate血e o匝ct.

26. Should a bowling ba11 rolling toward pins be treated as a point mass or an extended o車ject?

27. What is the main di飾erence between mass and moment ofinertia?

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Ⅱ): A

Ⅵrsion OOl - rO七ational motion free response - riegert - (8rieger七)　　　fi

This print置Ou七　Should have 7 ques七ions.

Mul七iple-Choice ques七ions may con七inue on

七he next column or page一缶nd all choices

b e魚〕reトanSWerlng・

Angular Position of a Whee1001 10.Opoint§

At t = 0, aWheel ro七ating about afixed axis a七

a 。。nS七a血angular deceleration of O.37 rad/s2

has an angular velocity of l.5 rad/s and an

anguhr position′ Of,了D重ね

What is the angular position of the wheel

a航er 2 s?

Answer in units of rad.

Grinding Wheel RotationOO2 (part l of2) 10.O points

A grinding wheel言出ially at res七言S`旗手

t,a七ed with constant anguIar acceIeration of

2.7 rad/s2 for 7:28 s. The wheel is then

brough吊o res七with u血fom deceleration in

4.69 rev.

Find the angular acceleration required to

bring the wheel to rest. No七e tha七an m-

crease in ang山ar veloci七y is cousistent with a

positive angular acceleration.

Answ。r in units of rad/s2.

003 (p紳士2 0f2) 10・O poi血s

De七emine the time needed to bring the wheel

七〇 res七.

Answer in uni七s of s.

APB 1998MC 68004　10.Opoints

A rod can pivot at one end and is free to

rotate without friction about a ver七ical axis)

as shoun. Å force, F is applied a‘t the・Other

end, at an ang土e O to the rod・

If F were to be applied perpendicular to

七he rod, at Wha七distance d from the axis

of rotation should it be applied in order to

produce the same t,Orque F?

1.d二LsinO

2.d=L七anO

3.d=LcosO

4.d二J豆L

馬.、虎=L

APM1998MC 5005　10.Opoints

A sys七em of two wheels fixed to each o七her is

free to rotate abou七a frictionless axis through

七he common ce血er of the wheels and per-

p甜dieular to‘ the p瞬・ F(那一fo雌eS a腱e汀

erted tangentf蘭y to the rins of、七he wheels・

念s shcywn below.

F

What is the magni七ude of the ne七torque on

the system alJOu吊he axis?

1.T二14F月

2.丁=2F廓

3・.千二5ず用

4.T=0

5.丁二F兄

Holt SF O8Rev 45

006　10.Opoin七s

A wooden bucket糾しed with water has a mass

of 71 kg and is attached ‘tO a rOPe that is

wound around a cylinder wi七h a ra’dius of

o.074 m. A crank with a tuming radius of

o.37 m is at七ached to the end ofthe cylinder.

what minimum force directed perpendicu-

larly to the crank handle is required to raise