NA~E______________________________ SECTION _____

Physics 211 Quiz 9

Answer the questions below in the space provided. Make sure you show all your work and any equations that you use. Please place a box around your answers, and remember to give the correct units with all numerical answers.

Disk Oscillator

A disk of mass M and radius R is pivoted at a point P on its rim. What is the period of small oscillations?

(Hint: The moment of inertia of a disk around its center of mass is MR2j2, and the parallel axis theorem provides you with a way to find the moment of inertia about point P in the figure above. You might also expect the answer to bear some similarity to but be different from the oscillation frequency of a simple pendulum which ~s given on the formula sheet.)

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NA~E_______________________________ SECTION _____

Physics 211 Quiz 9

Answer the questions below in the space provided. Make sure you show all your work and any equations that you use. Please place a box around your answers, and remember to give the correct units with all numerical answers.

Offset Stick Pendulum

A stick of mass M and length L is suspended from a frictionless rod inserted through a small hole % of its length from the top of the stick. It is displaced slightly from its equilibrium position and set into oscillation. What is the angular frequency of small-amplitude oscillations about the equilibrium position of the stick?

(Hint: To start with, draw a picture! Recall that the moment of inertia of a thin rod of mass M and length L, about a perpendicular axis through its center, is ML2j12, and that the parallel axis theorem lets you find the moment of inertia about another axis such as the one in this problem. You might also expect the answer to bear some similarity to but be different from the oscillation frequency of a simple pendulum which is given on the formula sheet.)

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L L e. ~ :::!::.. ~~.t 6'vVlA \tet ~.K/~ ~~~ rUVf eM 4' /~

L'~-I..I ~ ~t\1 L\. f- ML~r ;}II L"'(!? t-/,)

~

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tV}.:3 Sf;'" e r,- 9 \ e ;:: - - - ~/YI7 L

2- 1\11 L1­

Sl~ f} ~ e- ~,~~ f( ~ ( M ltt~{ tAt ~ 1"4 ~t(,d'.( JJ

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NA~E_______________________________ SECTION _____

Physics 211 Quiz 9

Answer the following questions, justifying your answer with either words or mathematics.

Conceptual: Ball Swing

A tiny ball is placed on the end of a string, pulled back to a small angle, and released from rest. The ball is then free to swing back and forth.

1) At what position in the swing will the magnitude of the angular acceleration of the ball be the largest?

0..4- tk ~~\w\fAf\A ~ I ~ I~ ~~~

eX ;"- ! (3. L

2) If the string were lengthened, the time to reach the release position would be

a10nger than in the original situation s,,, t( G<J""If l L~the same as in the original situation c) shorter than in the original situation

~ ,~'-'rr:~&..J N ckt.rt~J..-t.d

3) If the mass of the ball were increased, the time to reach the release position would be

a) longer than in the original situation 'w~ Ju~ ~J~ @ he same as in the original situation

c) shorter than in the original situation V'f'-M<l \ No k W fvve-~fV\~ ltk d:~ ~ weJE ~J.. ~~ ~ V'r--~.

NA~E______________________________ SECTION _____

Physics 211 Quiz 9

Answer the following questions, justifying your answer with either words or mathematics.

Conceptual: Sliding Block

A block of mass m is attached to a wall with an ideal spring. The mass is pulled back a distance xo from its equilibrium point and released from rest on a frictionless surface. Answer the following questions about the motion of the block.

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~ 1) At what position in the motion would the block have the largest magnitude of

accelera tion? 0.1 t X 'S ,-"., CA- m7l. ::: - J< X - OJ

2) If the block were instead released from a distance of 2xo, the time for the block to return to its release position would be

a} longer than the original oscillation @he same as the original oscillation :;,;" afret:"'-"':~ -'\>4 I~~J-/

c) shorter than the original oscillation I!I t 0- ""'f t<:~ IAJ.a.:; w:=Jf:./:' ~V Sf~' ( ,NQ k: tbv pC.;1 Je,,J t-tw

Q.) oc JiiTi..' 3) If the mass of the block were doubled but still released from xo, the time for the block to return to its release position would be

@ onger than the original oscillation ~ I.d~ w)Ic/I<-': b) the same as the original oscillation

M VWW ~ v1A.'-' I~,c) shorter than the original oscillation