Download Homework Packet Circular Motion Worksheet #1

Homework Packet Circular Motion
Worksheet #1 - Circular Motion Part 1 – Circular Motion Equations
1. The tires on a new car have a diameter of 2.0 ft and are warranted for 60,000 miles.
a. Determine the angle (in radians) through which one of these tires will rotate during
the warranty period. (5280 ft = 1 mi)
b. How many revolutions will the tire make while under warranty?
2. A CD accelerates uniformly from rest to its operational speed of 500 rpm in 3.50s.
a) What is the angular acceleration of the CD during this time?
b) What is the angular acceleration after this start-up time?
c) If the CD comes uniformly to a stop in 4.50 s, what is its angular acceleration
during that part of the motion?
3. A centrifuge in a medical laboratory rotates at an angular speed of 3,600 rev/min. When
switched off it rotates through 50.0 revolutions before coming to rest. Find the constant
angular acceleration of the centrifuge.
4. A microwave oven has a 30. cm diameter rotating plate for even cooking. The plate
accelerates from rest at a uniform rate of 0.87 rad/s2 for 0.50 s before reading its
constant operational speed.
a. How many revolutions does the plate make before reaching its operational speed?
b. What are the operational angular speed of the plate and the tangential (linear)
speed at its rim?
5. A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin
starts out with an initial angular speed on 18.0 rad/s and rolls in a straight line without
slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s2, how
far does the coin roll before coming to rest?
6. An airplane propeller slows from an initial angular speed of 12.5 rev/s to a final angular
speed of 5.00 rev/s. During this process, the propeller rotates through 21.0 revolutions.
What is the angular acceleration of the propeller in rad/s2?
Worksheet #2 - Circular Motion Part II – Centripetal Force
1. An Indy car with a speed of 120 km/h goes around a level, circular track with a radius of 1.00 km. What
is the centripetal acceleration of the car?
2. Find the centripetal acceleration for each of the following:
(a) a point on the earth’s equator (ignore its orbital motion) (radius of Earth=6.38x106 m)
(b) the earth in its orbit around the sun (radius = 1.49x1011 m)
(c) the sun’s orbit around the center of the Milky Way (period = 2 x108yrs; radius = 3 x1020 m)
3. A doughnut shaped space station has an outer rim of radius of 1 km. With what period should it rotate
for a person at the rim to experience an acceleration of g/5? (Remember: g = 9.8 m/s2)
4. A stone moves in a circle of radius 60 cm and has a centripetal acceleration of 90 m/s2. How long does it
take to make 8 revolutions?
5. A car approaches a level, circular curve with a radius of 45.0 m. When the concrete pavement is dry the
coefficient of friction is 1.20. What is the maximum speed at which the car can negotiate the curve at a
constant speed?
6. A laboratory centrifuge operates at a rotational speed of 12,000 rpm (rev/min).
a)
What is the magnitude of the centripetal acceleration of a red blood cell at a radian distance of
8.00 cm from the centrifuge’s axis of rotation?
b) How does the acceleration compare with g?
7. A 1.0 m cord is used to suspend a 0.50 kg tetherball from the top of the pole. After being hit several
times, the ball goes around the pole in uniform circular motion with a tangential speed of 1.1 m/s at an
angle of 20o relative to the pole.
a) The force that supplies the centripetal acceleration is (1) the weight, or (2) a component of the
tension force in the string, or (3) the total tension in the string. Pick one and explain why.
b) What is the magnitude of the centripetal force?
8. A student is to swing a bucket of water in a vertical circle without spilling any.
a) Explain how/why this task is possible.
b) If the distance from this shoulder to the center of mass of the bucket (ie. radius of the circle) is
1.0 m, what is the minimum speed required to keep the water from coming out of the bucket at
the top of the swing?
Worksheet #3 – Gravity Pulling it all Together
1.
Mass of Earth = 6.0 x1024 kg
Radius of Earth = 6.4 x106 m
Mass of Moon = 7.4 x1022 kg
Distance from Earth to Moon = 3.8 x108 m
Mass of Sun = 2.0 x1030 kg
Distance from Earth to Sun = 1.5 x1011m
If the mass of Earth were to be doubled at the same time the radius was doubled, the free-fall
acceleration would (a) increase, (b) decrease, (c) stay the same? Why?
2. Why does an astronaut in a spacecraft orbiting Earth experience a feeling of weightlessness?
3. Calculate the effective value of g on the top of Mount Everest, 8850 m above sea level.
4. A 50.0 kg person and a 75.0 kg person are sitting on a bench 50. cm apart. Calculate the magnitude
of the gravitational force each exerts on the other.
5. Most of the stars in the galaxy of which the sun is a member (the “Milky Way”) are concentrated in
an assembly about 100,000 light-years across whose shape is roughly that of a fried egg. The sun is
about 30,000 light-years from the center of the galaxy, and revolves around it with a period of
about 2x108 years. A reasonable estimate for the mass of the galaxy may be obtained by
considering this mass to be concentrated at the galactic center with the sun revolving around it like
a planet around the sun.
a.
On this basis, calculate the mass of the galaxy. (1 year = 3.15x107 sec., 1 light year =
9.46x1015 m)
b. How many stars having the mass of the sun is this equivalent to?
6. During a solar eclipse the moon comes between the Earth and the Sun.
a. Find the net force on the Moon due to the gravitational attraction of both the Earth and
the Sun when they are aligned Earth, Moon, Sun.
b. One fine day, the Star Ship Enterprise decides to tow the Earth out of its orbit and into
deep space. Will our Moon come with us? Explain.
7. Some communication and weather satellites are launched into circular orbits above the Earth’s
equator so they are synchronous with the Earth’s orbit. That is they remain “fixed” or “hover” over
one point on the equator. At what altitude are these geosynchronous satellites?
Worksheet #4
No equations or constants will be given for the test. You must handwrite everything you think you will need on
the front side of a 3x5 inch index card (one side only)
1.
A car is negotiating a flat curve of radius of 50.0 m with a speed of 20.0 m/s. The centripetal force provided
by friction is 1.20 x 104 N. What is the mass of the car? (1,500kg)
2.
What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when
the bike is moving 8.0 m/s? (180 m/s2)
3.
A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn at 96.5 km/h. What is the centripetal
force on the motorcycle? (13 kN)
4.
A 5.00 kg mass is attached to the end of a 1.00 m string. The system is whirled in a vertical circular path. If
the maximum tension that the string can withstand is 350. N. Where is the tension in the string the most?
What is the maximum speed of the mass if the string is not to break? (7.75 m/s)
5.
A car goes around a flat curve of radius 50.0 m at a speed of 14.0 m/s. What must be the minimum coefficient
of friction between the tires and the road for the car to make the turn? (0.4)
6.
The hydrogen atom consists of a proton of mass 1.67 x 10-27kg and an orbiting electron of mass 9.11 x 10-31kg.
In one of its orbits, the electron is 5.3 x 10-11m from the proton. What is the mutual gravitational attractive
force between the electron and proton? (3.61 x 10-47N)
7.
A satellite is in a low circular orbit about the earth (i.e. it just skims the surface of the earth). How long does
it take to make one revolution around the earth? (the mean radius of the earth is 6.38 x 106 m, mass of the
Earth = 6.0 x 1024 kg) (5,061s)
8.
A satellite is in circular orbit 230 km above the surface of the earth. It is observed to have a period of 89.0
min. From this information, calculate the mass of the earth. (the mean radius of the earth is 6.38 x 106 m)
(6.0 x 1024 kg)
9.
A wheel accelerates with a constant angular acceleration of 3.5 rad/s2. If the initial angular velocity is 2.0
rad/s, what is the angle the wheel rotates through in 2.0 seconds? (11 rad)
10. A ferris wheel rotating at 20.0 rad/s decelerates with a constant angular acceleration of –5.0 rad/s2. How
many revolutions does it rotate before coming to rest? (6.37 rev)