Conservation of Angular Momentum
Explain how angular momentum is conserved when a girl on a rotating merry go round moves towards the center and it starts rotating faster.
1) By moving towards the center of the merry-go-round, the girl reduces the system's rotational inertia.
2) The angular before she moves is equal to the angular momentum after she moves.
3) Angular momentum = Iω
4) As 'I' decreases, 'ω' increases.
What is required to change an object's rotational motion?
A torque.
Superposition occurs in which types of waves?
A wave with frequency moves along a string with a speed of 30 m/s.
If the frequency of the wave is doubled, what would the speed of the new wave be?
The same as before, 30m/s.
Wave speed is determined by the medium, not the wavelength or frequency.
An object rotating at 6 rev/s receives a torque which causes an angular acceleration of 4 rev/s2. If this torque acts on the wheen for 5 seconds, what is the final rotational velocity of the object?
ω =ω0+αt
= 6 + (4x5)
= 26 rev/s
Explain how angular momentum is conserved when a boy spinning a ball on a string gradually shortens the string, bringing the rotating ball closer to him.
1) By shortening the string, and moving the mass (the ball) closer to the center, the boy reduces the system's rotational inertia.
2) The angular before he shortens the string is equal to the angular momentum after he shortens the string.
3) Angular momentum = Iω
4) As 'I' decreases, 'ω' increases.
Which of the following correctly describes the quantities listed.
Torque, Rotational acceleration, Angular momentum
a) scalar, vector, vector
b) scalar, scalar, vector
c) vector, vector, vector
d) vector, vector, scalar
e) vector, scalar, vector
Torque, Rotational acceleration, Angular momentum
c) vector, vector, vector
A wave X meters long passes through a medium with a speed of Y meters per second. The frequency of the wave could be expressed as
a. Y/X cycles/sec. | b. X/Y cycles/sec. | c. XY cycles/sec. | d. (X + Y) cycles/sec. |
a. Y/X cycles/sec.
What is the period of a wave that has a speed of 0.4 m/s and a wavelength of 0.020 meters?
v = λ/T
T = λ /v = 0.02/0.4
T = 0.05s
What is the linear speed of an object that is at the end of 2m long stick that's rotating at 2 rev/s?
v = rω
v = 2 x (2π x2)
v = 25.1 m/s
How is angular momentum conserved in Kepler’s second law?
1) Kepler's second law states that planets move faster as they move closer to the sun.
2) As the planets move closer to the sun, their rotational inertia decreases. (I = mr2)
3) The angular before the planet moves closer is equal to the angular momentum after the planet moves closer.
3) Angular momentum = Iω
4) As 'I' decreases, 'ω' increases.
Why can't you open a door by pushing on its hinged side?
a. The lever arm is zero
b. the torque is zero
c. The force you applied was too small
d. both a and b are correct
e. a, b and c are correct.
d. both a and b are correct
SEE PPT.
Consider the standing wave pattern shown. A wave generated at the left end of the medium undergoes reflection at the fixed end on the right side of the medium. The number of antinodes in the diagram is _____
6
What is the mass of a 3m long string on a which a pulse travels at 30 m/s when the tension on it is 60N?
m = LF/ v2
m = 3x60 / 302
m = 0.2kg
A boy is holding his younger sister by the feet and spinning her around. The total rotational inertia of the two boys is 50kgm2. The boy then pulls his arms closer, reducing the rotational inertia of the system to 40kgm2. What is the change in angular momentum of the system?
No change.
Angular momentum is conserved.
Explain why when a boy sitting on a chair that can rotate holding a rotating bike wheel turns it over, he starts rotating.
1) If the wheel is spinning counter-clockwise, the initial angular momentum is upwards.
2) After turning the wheel over, the wheel is rotating counter-clockwise and the angular momentum is downwards.
3) Because angular momentum is conserved, the magnitude and direction of the angular momentum after must be equal to the magnitude and direction of the angular momentum before the wheel was turned over.
4) The chair starts rotating counter-clockwise to make the total angular momentum upwards.
Why do you put your arms out to both sides of your body when trying to balance on a narrow surface?
Putting your arms out moves mass away from the axis of rotation, increasing moment of inertia and thus increasing resistance to angular acceleration (i.e. losing balance)
Many wave properties are dependent upon other wave properties. Yet, one wave property is independent of all other wave properties. Which one of the following properties of a wave is independent of all the others?
a. wavelength | b. frequency | c. period | d. velocity |
Answer: D
The speed of a wave is dependent upon the properties of the medium through which it moves, not upon the properties of the wave itself.
A standing wave with 4 nodes is created on a rope that is 3m long. What is the wavelength of the standing wave?
4 nodes = 3rd harmonic
At third harmonic λ = 2/3L
λ =2/3 x 3 = 2m
How much is the kinetic energy of an object increased by if the angular velocity of that object is increased by 10%?
KER = 1/2 Iω2
ω -> 1.1ω
ω is squared in the equation, so 1.12 = 1.21
K.E is increased by 21%
Why does a wheel hanging on a string which is rotating counter-clockwise vertically start rotating horizontally as well?
1) The weight of the wheel causes a torque and therefore rotation in the wheel.
2) This causes the angular momentum to change direction downwards.
3) As angular momentum must be conserved, the wheel starts rotating counter-clockwise horizontally to balance the change in momentum.
See PPT.
A wheel of outer radius R has an axle of radius R/6. Strings are wrapped as shown around the rim of the wheel and around the axle. If the string around the rim of the wheel has tension T, then in order to keep the wheel from turning the tension in the string around the axle must be:
a. 6T
b. 6Tsinθ
c. T/6
d.(T/6)sinθ
a. 6T.
We want torque to be equal to zero.
The diagram shows a disturbance moving through a rope towards the right. If this disturbance meets a similar disturbance moving to the left, then which one of the diagrams below depict a pattern which could NEVER appear in the rope?
D could never happen
A second harmonic standing wave is created in a 0.3m long pipe with one closed end.
What is the frequency of the wave?
For second harmonic,
λ = 4/3L
λ = 0.4m
f = v/λ
f = 340/0.4 = 850Hz
You spin a bicycle wheel (diameter of 0.85 m, mass of 4.5 kg), applying a force of 24 N tangentially. Assuming the wheel is a thin-walled hollow cylinder, find the angular acceleration of the wheel.
τ = FL = 24 x 0.425 = 20.4Nm
I = mr2 = 4.5x0.4252 = 0.813kgm2
α = τ/I = 20.4 / 0.813 = 12.5 rad/s2