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Faculty of ENPH 131 Last Name: '$D to -1tlJYl ~ Engineering Seminar 11 First Name: _________________

Angular Momentum/Rotation and of Rigid Bodies ID Number:___________

Department of Physics Seminar Section:

This seminar is not to be handed in - you are still responsible for this material.

1. In the figure shown below, there are five particles moving in the standard x - y plane with the origin

at O. Particles 1 and 2 move on circular paths about point 0 in opposite directions, with radii 4 m and

2 m, respectively. Particles 3 and 4 travel in the same direction along lines at perpendicular distances

4 m and 2 m from point O. Particle 5 moves directly away from point O. All particles have the same

mass and same constant speed. As usual, the positive z - direction is out of the plane (towards you).

<l _ , - -- I 1>--- ---- - ------ ­P .; ....../' I '.. 3

/ "­I ' I ./...... \

I (/ '\ \

II ( 0 . \ \ 0.- - --. t>- ­\ I [)\ \ / I

\ "- /' /\ <l > , -- I --- -- - --- - -- 1 t>---­"- 2 / 4" /

......... ~ - - - ~ /

a) Rank the particles according to the magnitude of their angular momentum about point O.

Rank them from greatest to least and indicate any ties.

Answer: , -== 3) 2 ::::- 4-) S-b) Which of the particles have a negative angular momentum about point O?

Answer: 2 C. n d 3

d rYlu-::::: 4-mu5 = -+ L--\-mLJPI : (Hc)t ~ )

- 2VhlJPL LH")t ~ d1..)'\,1 L.r ~ Lmu- (J.. r

- ~ L\-mu p~ ; (Ho)~ cl)rnLJ'=- 4-MuC

2 mu-- 5 T2h1u :::. d~ VY\ u -::p~ -: lHo)~

MU-=- DP5°- C(10) h -::: ds

2. The body shown below is pinned and free to rotate about point O. Three forces act on it in the

directions shown:

.,

:

FA =ION at point A 8.0 m from 0

Fa = I6N at point B 4.0 m from 0

Fe = I9N at point C 3.0 m from 0

What is the net moment (torque) about point O? Express your answer as a magnitude and direction as

either clockwise or counter-clockwise.

A - eMO)f+ ~ r A x FIT

tyI~ Yl i ivde: fA FA- 'Sivl Y 51) :::- (B)( ID) "5I104S o =- Sb, ~T ~, tv)

d I~C-h-oY\ : 5 ( (? isht Ku..-d r<u le)

b : ( rVI 0 ) ~ = ("'8 >I- F~ m 4:JVli +Ode ; ('E, F.e. SI 90' - (4') Clt;)sIYlqo 0 = b if N' m

dCfec.-h IY\!. C VV\ \ -::2 r c x. F<­

( _I'IO)L - ­

de; I e FeVYlC<~V)1 .

I

/ /

d(yt'cffLY) ~ !J

3. A uniform wheel (pulley) of radius 0.20 m is mounted on a frictionless horizontal axle. The moment

of inertia of the wheel about this axis is 0.050 kg· m2• A massless cord wrapped around the wheel is

attached to a 2.0 kg block that slides on a smooth horizontal surface.

p

If a horizontal force of magnitude P = 3.0 N is applied to the block, and the cord does not slip on the

pulley, determine the following:

a) the acceleration of the block;

b) the angular acceleration of the wheel (pulley); ) c) the tension in the cord between the block and the pulley. (Wlc:J 'I" -/vd-e

TY)g5 r---+----,.

p

fbO /KO

p / /

0,0'5 \ 1- 2( 0, 22.. )

'"3

3 ,2S

I

)0)e j ole 1- ~ b ~ S \ cc. t~ da I\e ;:.

eX=: ~ ~ 0, crL~\ ==- 4 t b (6 V'ud! S l­

y- 0, 2

T :::: TD ~ _ (Of050) ( 0, c::r23l) =- Iv IS Y- V\J ' ("''2- 0, 2 2..

a ) Q :::: O. q2~ h) /s"L ~

b) 0/ = 41 b L ~ /5'- C C-) -r l, I S- rJ