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15/ Fall 2003 Last Name________________________. Physics 175 Exam #3 First Name______________________._
ID # Points for each question are indicated in parentheses. Show your work for solutions to questions that
require calculations. Explain from where you start to solve the problem and show your math ﬂowing
from it for full credit. Surround your result in a box and don ’t forget to include the units for your result.
If you need more space to ﬁnish a question, write BPP (Back of the Previous Page) at the end of the
space provided and then complete your work on the back of the previous page. For multiple choice
questions, circle the letter which you believe to be correct (or best). In all problems, take the gravitational acceleration g = 10 m/sz. 1. (3 points) Consider the system of coupled wheels shown in the ﬁgure at right. The
radius of wheel A is one half of that of wheel C. If wheel C is rotating at a constant
angular speed of 100 rev/min, and assuming the belt does not slip, which of the
following statements is correct. a) The angular speed of A is half of the angular speed of C.
b) The linear speed at the edge of wheel C is half of that at the edge of wheel A. c) The angular speed of A is varying with time.
The acceleration felt on both wheels is zero. The angular speed of A is twice that of C. 2. (3 points) You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis
pdicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted on it by gravity is: 0
b) mgr
c) 2mgr
d) a ﬁmction of the angular velocity
e) small at ﬁrst, then increasing as the Frisbee loses the torque given it by your hand 3. (3 points) A girl stands on the edge of a merrygo—round which is initially rotating without friction at
constant angular speed. If she walks radially inward toward the center of the merrygoround, which of the following best describes what happens to the system during this process?
a) the angular momentum and the moment of inertia of the system both decrease and the angular speed increases
b) the angular momentum increases while the moment of inertia and the angular speed both remain constant
c the angular speed, the angular momentum, and the moment of inertia all decrease the moment of inertia decreases, the angular speed increases, and the angular momentum remains constant
e) the angular speed decreases while the moment of inertia and the angular momentum remain constant 4. (3 points) An astronaut with weight W on E
Earth and radius 0.5 times the radius of Earth. Th a) 002W H .W .N . HG N L( w
.b).0.04w \X} a (9 J—' : 9 Z [9 1.. , , 0
c 0.2w , l’ ’2; (0.626} kg 0.25
0.4w
W .9 ive direction with a velocity of v. It collides headon
e opposite direction. If the two objects stick
of the combined object after the collision? 5. (3 points) An object of mass m moves in the posit
with an object of mass 3m moving with speed 2v/ 3 in th
together, what is the velocity (magnitude and direction) a) 0 b) 3v/4 YV\\oL"6\IV\'D/':;;H: = {w—t’iynkw‘ c) v/4 3+
d) 3v/4 ma—zng: wa‘ 97 a“; , E v/4 6. (10 points) True or false:
Tglgg a) If the angular velocity of an object
zero at that instant.
True, b) The moment of inertia of an object
Twig c) When an object rolls without slipping,
T‘f‘ue d) If a particle moves in a straight line with co
point stays constant as it moves.
(Nut, 6) When a girl on a merry—goround throws a ball radially outward, the angular momentum of the girl plus merrygo—round remains constant. is zero at some instant, the net torque on the object must be depends on the location of the axis of rotation. friction does no work on the object.
nstant velocity, its angular momentum about any ﬁxed sitioned on a vertical axis. The bottom disk is 7. (5 points) Two identical disks are po
rotating at angular velocity (00 and has rotational kinetic energy K0. The top disk is
initially at rest. It is allowed to fall, and sticks to the bottom disk. What is the rotational kinetic energy of the system after the collision? £93112: Ko= liin ‘) Ewe; [filmb3 =3 bur—iii:
2 t 2 Z
c)Ko =Lﬁwglwz=iwo=L .~c_si
d) 2K0 ii 2} \ T“ l L z
e) “<0 K4,}. :2. 8. (5 points) The position vector of a particle of mass 3 kg is given by r = 4i + 3t2j, where r is in meters and t is in seconds. Determi fz’fﬁ? J‘lewﬁi =‘(\/\£\fﬁ‘<t
3=ﬁzfotA=7a (13% A
M 3 L=B L. 3% o vagrant
0 Cat 0 9. (10 points) A penci
table. The eraser does no
a) Find the moment of inert inertia when rotating around an axis through its center of mass is 12
an angle of 60° with the vertical? 1, 15 cm long,
t slip. Treat the pencil like a uniform is released from a vertical p ia of the pencil with respect to its ax osition with the eraser end resting on a rod. is of rotation, knowing that its moment of 1 MLZ. ::m\’ “(if WW <§~5£31
‘Z
1eéuf+v % :éhﬂ'
:Lw}
,/3—/
L
Uw" L
l L ,.
V%Mgiiw+ “0A; (Net)
L $03600 L_ Q30 2 ELL:
'3 9
L0ng %[l~ceséoB
lemme»
1w» l5. _
’ l— ‘ m5 ’ ‘00 = 2.0 m is attached to a wall at one end by a
= 1 kg is attached to the rod a distance 3L/4 pivot A and at the other end by a horizontal string. A mass m
with the wall. a) Draw all the forces from the pivot A. The rod is in static equilibrium at an angle of 53°
acting on the mg and build a free body diagram for it. v)
“‘3
b) Find the tension in the string and the magnitude and the direction of the force acting at pivot A. Take
sin 53° = 0.8 and cos 53° = 0.6. ,4 ﬂ (_ (_
21;;0 9) +3" \>0 a») +2;\ \ ll. ( 10 points) A student sits at rest on a piano stool that can rotate without friction. The moment of
inertia of the student stool system is 4 kg m2. A second student tosses a medicinal ball with a 2 kg mass
with a speed of 4.5 m/s to the student on the stool who catches it at a distance of 0.5 m from the axis of rotation. What is the resulting angular speed of the student and the stool? 1a? was“: LL: L4 a W”: (“isw'iuh'w N: 932%; weir: ler mt2\w
Av: L15 We
9 NW
\f‘: v m: f 1
int" “M
ma? f a
(A): 2443.05 P a L
14+ 7,0be
1103
we L "5' Bonus Question
At the grocery store you pick up a can of beef broth and a can of chunky beef stew. The cans are identical in diameter and weight. Rolling both of them down the aisle with the same initial speed, you notice that
the can of chunky stew rolls much farther than the can of broth. Why? The tom 6g Wer “Aug SLAM ax &0N§: W J: & gm Low We
(\MCSWQNV \th (“(595 owl/M) ...
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 Spring '08
 kozstin
 Physics, Angular Momentum, Moment Of Inertia, Rotation, rod

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