Download South Pasadena A.P. Physics Name Chapter 8 Rotational Motion

South Pasadena A.P. Physics
Chapter 8 Rotational Motion
Name ______________________________
Date ___/___/___ Period ____
“Practice Test”
1.
In an effort to tighten a bolt, a force F is
applied to a wrench. If the distance from the
end of the wrench to the center of the bolt is
20 cm and the applied perpendicular force
F = 20 N, what is the magnitude of the
torque produced by F?
a) 1 m ● N
c) 4 m ● N
b) 2 m ● N
d) 10 m ● N
2.
5.
m
M
A uniform meter stick of mass 1 kg is
hanging from a thread attached at the stick’s
midpoint. One block of mass m = 3 kg
hangs from the left end of the stick, and
another block, of unknown mass M, hangs
below the 80 cm mark on the meter stick. If
the stick remains at rest in the horizontal
position as shown above, what is M?
60
L
m
In the figure above, what is the torque about
the pendulum’s suspension point produced
by the weight of the bob, given that the
length of the pendulum, L is 80 cm and
m = 0.50 kg?
a) 0.5 m ● N
c) 1.7 m ● N
b) 1.0 m ● N
d) 2.0 m ● N
a) 4 kg
c) 6 kg
b) 5 kg
d) 8 kg
6. A carousel a 6FM2 (Six Flags Magic
Mountain) accelerates from rest to an
angular velocity of 0.3 rad/s in a time of 10
seconds.
a) What is the angular acceleration(α)?
b) What is the linear acceleration for a
point at the outer edge of the carousel, at
a radius of 2.5 m from the axis of
rotation?
3. Convert 90° to radians
4. Convert 6 radians to degrees
7. How many complete rotations does the
carousel make while accelerating to its
maximum angular velocity?
8. Calculate the moment of inertia (I) for a
bowling ball (solid sphere) with a mass of
10 kg and a radius of 0.2 m. (I = 2/5 mr2)
9. Find the moment of inertia (I) of two 5 kg
bowling balls joined by a 1-meter long rod
of negligible mass when rotated about the
center of the rod. Compare this to the
moment of inertia of the object when rotated
about one of the masses. (The moment of
inertia of each ball will be considered as
mr2 since they are not rolling, but rotating. r
is not the radius of the ball but the lever arm
distance.) CAN YOU GUESS WHICH
ONE WILL HAVE A LARGER VALUE?
5 kg
11. Angelina spins on a rotating pedestal with
an angular velocity of 8 radians per second.
Bob throws her an exercise ball, which
increases her moment of inertia from
2 kg ● m2 to 2.5 kg ● m2. What is
Angelina’s angular velocity after catching
the exercise ball? (Neglect any external
torque from the ball.)
12. A 3-kilogram café sign is hung from a 1kilogram horizontal pole as shown in the
diagram. A wire is attached to prevent the
sign from rotating. Find the tension in the
wire. (This problem is similar to the torque
hinge lab done in class)
5 kg
30
3m
5 kg
5 kg
10. Gina rolls a bowling ball of mass 7 kg and
radius 10.9 cm down a lane with a velocity
of 6 m/s. Find the rotational kinetic energy
of the bowling ball, assuming it does not
slip. (I for a solid sphere is 2/5 mr2)
1m
3 kg
13. Convert 1.5 revolutions to both radians and
degrees.
14. A record spins on a phonograph at 33 rpm
clockwise. Find the angular velocity, ω, of
the record. Let clockwise be the negative
direction and counter clockwise be the
positive direction.
15. Find the magnitude of the Earth’s angular
velocity in radians per second.
16. A frog rides a unicycle that begins at rest,
and accelerates uniformly in a counterclockwise direction to an angular velocity of
15 rpm in a time of 6.0 seconds. What is the
angular acceleration, , of the unicycle
wheel?
17. A knight swings a mace of radius 1 m in two
complete revolutions. What is the distance,
l, traveled by the mace?
18. A compact disc (CD) player is designed to
vary the disc’s rotational velocity so that the
point being read by the laser moves at a
linear velocity of 1.25 m/s. What is the
CD’s rotational velocity in rot/s when the
laser is reading information on an inner
portion of the disc at a radius of 0.030 m?
19. What is the rotational velocity of the
compact disc in the previous problem when
the laser is reading the outermost portion of
the disc (radius = 0.06 m)?
More Torque Problems
20. A captain of a ship takes the helm and turns
the wheel of his ship by applying a force of
20 N to the wheel spoke. If he applies the
force at a radius of 0.2 m from the axis of
rotation, at an angle of 80° to the line of
action, what torque does he apply to the
wheel?
21. A mechanic tightens the lugs on a tire by
applying a torque of 110 m-N at an angle of
90° to the line of action. What force is
applied if the wrench is 0.4 meters long?
22. What is the minimum length of the wrench
if the mechanic is only capable of applying a
force of 200 N?
23. A variety of masses are attached at different
point to a uniform beam attached to a pivot.
Rank the angular accelerations (α) of the
beam from largest to smallest.
A
•
2M
B
•
3M
C
D
•
2M
M
M
2M
•
24. A 10-kg tortoise sits on a see-saw 1 meter
from the fulcrum. Where must a 2-kg hare
(rabbit) sit in order to maintain rotational
equilibrium? Assume the see-saw is
massless. (First Draw a Diagram)
28. An object with uniform mass density is
rotated about an axle, which may be in
position A, B, C, or D. Rank the object’s
moment of inertia from smallest to largest
based on axle position.
D
•
•
Moment of Inertia (or Rotational Inertia)
25. Calculate the moment of inertia for a hollow
sphere with a mass of 10 kg and a radius of
0.2 m. Compare this answer to the answer
to question #8. (Look up the formula for a
hollow sphere in your textbook.)
26. Calculate the moment of inertia for a long
thin rod with a mass of 2 kg and a length of
1 m rotating around the center of its length.
(Look up the formula for a long thin rod in
your textbook.)
27. Calculate the moment of inertia for a long
thin rod with a mass of 2 kg and a length of
1 m rotating about its end. (Look up the
formula in your textbook.) How does this
answer compare to the previous answer in
#26?
C
A
•
•
B
29. What is the angular acceleration experienced
by a uniform solid disc of mass 2-kg and
radius 0.1 m when a net torque of 10 m•N is
applied? Assume the disc spins about its
center.
(Hint: Just as Fnet = ma τnet = I α)
and Idisc = ½ mr2)
30. A merry-go-round on a playground with a
moment of inertia of 100 kg•m2 starts at rest
and is accelerated by a force of 150 N at a
radius of 1 m from its center. If this force is
applied at an angle of 90° from the line of
action for a time of 0.5 seconds, what is the
final rotational velocity, ω, of the merry-goround?
Hint: First find torque, τ, then find α,
then find ω.
Answers:
12. First show all of the forces on the pole as a
means to illustrate the various torques.
Assume the pivot is the attachment point on
the left hand side of the pole.
1. c)
2. d)
There are two torques acting downward or
clockwise and one torque acting upwards or
counterclockwise. The sum of these three
torques is zero since the pole is in
equilibrium. (g = 9.8 m/s2)
3. 1.57 rad
4. 344 °
5. b)
6. α = 0.3 rad/s = 0.03 rad/s2
10 s
and a =r = 0.075 m/s2
τ net = τ up – τ1 down − τ2 down =
T sin 30 (4m) – (3 kg)(g)(3 m) – (1 kg) (g) (2
m) = 0
7.  = ½ α t2 = 1.5 radians
T = 11 kg ● m x g = 54 N
4 m sin 30 
1.5 radians x 1rot/2πradians = 0.24 rotations
13.
9.42 radians and 540°
14.
‒ 3.46 rad/s
15.
7.27 x 10‒5 rad/s
16.
1.57 rad/s and 0.26 rad/s2
9. I = Σ mr2 = (5 kg)(0.5 m)2 + (5 kg)(0.5 m)2
= 2.5 kg ● m2
17.
l = r θ = 12.6 m
18.
ω = v/r = 41.7 rad/s = 6.63 rot/s
I = Σ mr2 = (5 kg)(1m)2 + (5 kg)(0 m)2
= 5.0 kg ● m2
19.
20.8 rad/s and 3.32 rot/s
20.
τ = r F sin θ = 3.94 m•N
21.
275 N
22.
0.55 m
23.
D, C, A, B
24.
5 m from fulcrum
25.
0.27 kg ● m2
= ½ (0.0333 kg ● m2) (55 rad/s)2
26.
0.17 kg ● m2
= 50.4 Joules
27.
0.67 kg ● m2
28.
C, B, D, A
29.
1,000 rad/s2
30.
τ = 150 m•N and α = 1.5 rad/s2
and ω = 0.75 rad/s
8. I = 0.16 kg ● m2
10. I = 2/5 mr2 = 2/5 (7 kg) ((0.109 m)2
= 0.0333 kg ● m2
ω = v/r = 6 m/s / 0.109 m = 55 rad/second
K.E. rot = ½ I ω2
11. L0 = L
or
I0 ω0 = I ω
ω = I0 ω0 = (2.0 kg ● m2) (8 rad/s)
I
2.5 kg ● m2
= 6.4 rad/s