2nd Semester Review Key
Uniform Circular Motion
In Unit 6 we examined objects in circular motion which were moving at a constant speed, but
experiencing a net inward acceleration due to the constant change in direction. The acceleration
toward the center of the circle results in a net force towards the center. You should be able to convert
from radians to degrees and find the angular velocity and acceleration of spinning objects. You should
also be able to solve for any forces acting on the rotating object.
Example:
Example:
1. Convert the following angles from degrees to radians.
a. 10˚
b. 45˚
a. .174 rad
b. .785
2. Convert the following angles from radians to degrees.
a. π/25 rad
b. π/10 rad
a. 7.2˚
b. 18˚
3. Izzy Dizzy is doing doughnuts in the mall parking lot. If his car is moving along a circular path
of radius 25.0 m at a speed of 15.0 m/s, what is the centripetal acceleration of Izzy and his
car?
A = V2/r A = (15m/s)2/25m, A= 9.0m/s2
4. At what constant speed would Izzy (mass 80 kg), have to be traveling in order to feel
weightless as he drives over the top of a hill with a radius of curvature of 20 meters?
Be sure to draw a force diagram to represent the situation.
∑ Fx = ma, Fn + Fe = ma, If he feels weightless then the Fn =0, so Fe = ma
-800 N = 80 kg V2/20 m, V = 14.1 m/s
5. Use Newton’s law of universal gravitation to determine the orbital period, in minutes, of a satellite
at an altitude of 320KM. MASS EARTH =5.98E24, RE=6.4E6
V= 7704 M/S,
THEN USE V=R ω
PER = 91.3 MIN
Torque
Torque is the result of a force acting at a distance from a rotational axis, and may cause a rotation about
the axis. You should be able to solve torque problems in static equilibrium and when things are
rotating.
Example:
1. A 20-kg board, set with its center on a support, serves as a seesaw for two children. One child has a
mass of 30 kg and sits 2.5 m from the support. A second child, who has mass 15 kg, sits at the other
end of the board at the same distance from the support. Where must a third child, of 20 kg, sit in order
to balance the board?
Τ1 = Τ2 + Τ3, (300 N )(2.5 m) = (150 N)(2.5 m) + (200 N) r,
r = 1.87 m
2. Look at any of the rotating problems on the More Torque worksheet
Fluids
Fluid dynamics is the study of substances that flow. Fluids can be either a gas or a liquid.
We examined pressure a fluid exerts on an object and the buoyant force provided by a fluid. We also
looked at the velocity of moving fluids in relation to the area of the container and at the Bernoulli
principle. You should be able to solve any of those type of problems.
Example:
1. A rectangular air mattress has a length of 2.0 m, a width of 0.50 m, and a thickness of 0.08 m. If the
mass of the material is 2.3 kg, what mass can just be supported by the mattress in water?
Bouyant Force = ρgV, Fb = 1000 kg/m3(10 N/kg)(2.0 m*0.5 m* .08 m), Fb = 800 N
The weight of the mattress downward is 23 N, so it could support a weight of 777 N before
sinking .
2. Look at the problems on Fluids WS#2
Simple Harmonic Motion (SHM)
When an object, such as a pendulum or mass on a spring, is oscillating or vibrating it is said to be in
Simple Harmonic Motion. To continue to oscillating there must be a restoring force continually
trying to restore it to equilibrium. If it’s a spring then it obeys Hooke’s law F=Kx
Amplitude (A) is the maximum displacement from equilibrium.
Frequency (f) is how many complete cycles per second the oscillator makes .
1
Period (T) is the number if seconds per one cycle, the inverse of frequency T =
𝑓
The period of a pendulum depends on the length of the string, NOT on the mass
The period of a mass on a spring depends on the mass and the spring constant
T=2𝜋√
T=2𝜋√
𝑙
𝑔
𝑚
𝑘
Q. What would happen to the period of a pendulum if you doubled the length of the string?
T=√2 or 1.4 times greater
Q. What would happen to the period of a spring oscillator if you double the spring constant?
T= √.5 OR .70 times greater
A
Fill in the graphs below for a mass, stretched
from equilibrium to the left and released so
that it oscillate
B
C
D
5.0 cm
E
5.0 cm
10.0 cm
10.0 cm
0
0
B
C
B
A
B
C
B
A
B
C
B
A
B
C
B
A
net force
A
acceleration
time
position
time
velocity
time
time
A
B
C
B
A
B
C
B
A
B
C
B
A
B
C
B
A
Waves and Sound
A wave is a disturbance in a medium. It is a way of transferring energy.
Wavelength λ - the distance from one point on a wave to the same point on the next wave. For example, from
crest to crest or trough to trough. Measured in meters.
Amplitude A – is the height of a crest or trough, measured from the equilibrium point in meters.
Frequency f – is how many wave pass a certain point in each period of time, usually waves/second or hertz.
Period T – is how many seconds for one wave to pass a certain point. The inverse of frequency, measured in
seconds.
Velocity v – the speed of a wave pulse. Depends on the medium through which the wave is traveling. The
only way to change wave speed is to change the medium.
Transverse wave-the wave pulse is perpendicular to the direction of pulse motion. For example, the
slinky/snakey, or ocean waves.
Longitudinal waves- the wave pulse is parallel to the direction of pulse motion. For example, sound waves.
Node-where a standing wave moves the least. (least amplitude). The quietest point on a sound wave.
Antinode-where a standing wave moves most (greatest amplitude). The loudest point on a sound wave.
You should be able to identify wave patterns by counting nodes and antinodes on a standing wave.
𝑣 = 𝑓𝜆
Q1. A weight on the end of a string bobs up and down one complete cycle every two seconds. Its period is
a. 0.5 sec.
b. 2 sec.
c. neither of these.
Q2. A weight suspended from a spring bobs up and down over a distance of 1 meter in two seconds. Its
frequency is
a. 0.5 hertz.
b. 1 hertz.
c. 2 hertz.
d. none of these.
Q3. You dip your finger repeatedly into water and make waves. If you dip your finger more frequently, the
wavelength of the waves
a. shortens.
b. lengthens.
c. stays the same.
Q4. A girl on the beach, watching the waves, sees 4 waves pass by in 2 seconds, each with a wavelength of
0.5m . The speed of the wave is
a. 0.25 m/s.
b. 0.50 m/s.
c. 1.0m/s
d. 2 m/s.
e. 4 m/s.
Q5. High pitched sound has a
a. high speed. b. high frequency. c. long wavelength. d. all of the above.
How can you use a column of air and a tuning fork to determine the speed of sound?
Sound-You should know how are frequency and amplitude are related to pitch and loudness for any sound
wave? You should also be able to calculate beat frequency.
Doppler effect- the apparent shift in frequency due to the motion of the source relative to the observer.
You should be able to determine if an observer would hear a higher or lower frequency and calculate the
1
new frequency. f ′ = f(1±v)
Interference
Diffraction is the bending of a wave around a barrier or through an opening. If we pass a light wave
through a narrow single slit, it will behave very similarly to water waves, with the edges of the light
waves lagging behind the center of the waves. If we place a screen opposite to the single-slit opening,
we would see a bright light near the center of the screen with smaller bright spots on either side. The
bright spots indicate constructive interference and the dark spots are destructive.
Use Young’s equation to solve for λ, d, L, or order.
𝜆
𝑑
=
𝑛𝑌
𝐿
or 𝑠𝑖𝑛𝜃 = 𝑛
𝑌
𝑑
Q Two sources, S1 and S2, are producing 2.0 cm wavelength waves. Destructive interference occurs at
point P, which happens to be on the second destructive line past the center (zero order) line. The
distance from S1 to P is 26 cm. What is the distance between S2 and P? Draw a sketch of the
situation.
λ=2.0cm, second destructive means 1.5 waves difference, so distance = 3.0cm
Refraction
Light can be refracted, or bent, when it passes from a medium of one density into another medium.
The speed of light changes in a medium according to the index of refraction, n, for that medium.
𝑛=
𝑐
, where c is the speed of light and v is the velocity in the medium. The angle of
𝑣
refraction, from the normal, follows Snell’s law 𝑛𝑠𝑖𝑛𝜃 = 𝑛𝑠𝑖𝑛𝜃 . You should be able to
sketch or identify a ray diagram, and calculate the angle of incident or refraction for a ray
passing from one medium to another.
Q. The critical angle for the liquid/air interface is 48°. What path
does light ray X take?
Path E, back into the water
Q. The ray is passing from water, n=1.33, into an unknown substance.
The incident ray is at 50˚ from the normal and the refracted is 60 ˚
Calculate n for the unknown substance. What is the speed of light
in this material?
N=1.18, speed of light = 2.3E8
Geometric optics: reflection in plane & curved mirrors- lenses
You should be able to sketch (or identify) a ray diagram for the image produced by plane mirror,
curved mirror or lens, and describe the characteristics of the images. For example, upright, virtual,
enlarged. You should also be able to distinguish between concave and convex mirrors; converging
and diverging lenses. Use the lens formula to determine do, di, or f given the the other two.
Use do & di to determine image size and magnification.
1
1
1
𝐼
𝐼𝑑
=
+
=
=𝑚
𝑓
𝑂𝑑
𝐼𝑑
𝑂
𝑂𝑑
Q. A converging (convex) lens has a focal length of 15.0 cm. A 5.0-cm tall candle is placed
at a distance of 40.0 cm to the left of the lens. Sketch the ray diagram and calculate the image distance
and size.
Id = 24cm, I= 3cm
f
f
Q. The 10.0 cm tall Easter Egg below represents your grade, sketch a ray diagram to show how your
grade actually appears after too many absences. The egg is 60 cm in front of a concave mirror with
focal length of 20 cm. Calculate the size and location of the image.
Id=30cm, I = 5cm
%
Electricity
Look at the E&M Unit 1 and 2 reviews on my web page under documents
Circuits
State Ohm’s Law; use it to solve for an unknown (voltage, current, resistance, or power)
in simple DC circuits.
Determine the resistance, current flow and voltage drop across two points in series and parallel
circuits.
Q. What is the current through an 8 ohm toaster when it is operating on 120V?
I=15a
Q. Determine the total resistance, total current, the voltage drop across each resistor and
the current through each resistor.
6.0 V
10Ω
15Ω
Rt = 5Ω, It=1.2a, I10=.6 Ω, I15=.4 Ω, I30=.2Ω
Rt = 18.6Ω , It=.32a,
V10=3.2v, I = .32a
V15=2.8v, I =.18a
V20= 2.8v, I = .14a
20Ω