Download Circular Motion Review Guide - North Allegheny School District

Circular Motion Study Guide
North Allegheny High School
Mr. Neff
An object moving in a circle with ________________ radius at ________________
speed is said to be undergoing ____________ ________________ ___________.
In this case, the object is ________________________ because it is constantly changing
its direction. This acceleration is pointed toward the ____________ of the circle, and so
we call it a _____________________ acceleration, an adjective that means
____________-____________. We know it is pointed toward the center, because
acceleration always points the same way as the ______ __________, which clearly
points toward the center. Because this net force causes this acceleration, we call it
______________________ force.
Centripetal force is not the ________ of a force; instead, it does not describe what type of
object is exerting the force, like normal force(the result of a bowed surface), tension force
(the result of a stretched string) or friction (the result of sliding of two irregular surfaces),
among others. Rather, the word centripetal on a force tells that the force is directed
toward the center of the circle. A good description of a centripetal force will have both
the word centripetal and the name of the force, like centripetal tension force (for a string
pulling an object in a circle), centripetal gravitation force (for a satellite being pulled in a
circular orbit), or a centripetal friction force (allowing a car to round a corner).
Some people also think objects in uniform circular motion also experience an outward
______________________ force. This is an ________________. When an object
moves in a circle, its inertia causes it to resist changes in its state of motion.
Consequently, the object attempts to (and will, without enough centripetal force) move to
the outside of the circle. When the moving object is a person, this inertial effect is easily
misinterpreted as a force to the outside, or a centrifugal force.
Centripetal acceleration depends ________________ on the ____________ of the
object’s speed and __________________ on the radius of the circle. Elegantly,
ac =
To get centripetal force from centripetal acceleration, simply multiply by the ________.
The ____________ of a rotating object is the time it takes to complete one rotation or
make one complete cycle. It is generally measured in _____________.
The __________________ of a rotating object is the number of complete rotations or
cycles completed in a time interval, usually ______ ____________, in which case the
unit is rotations/second or __________.
The relationship between period and frequency is that they are _____________________.
______________ ________________ is the rate of change of the ______________
angle of the rotating object. The central angle is the angle with its ____________ at the
center of the circle. The symbol for angular velocity is the ____, and it is usually
measured in ______________ per ____________.
What is the direction of the force that acts on the clothes in the spin cycle of a washing
machine? What exerts the force?
You are sitting on the back seas of a car that is going around a curve to the right. Sketch
a diagram to answer the following questions.
a. What is the direction of your acceleration?
b. What is the direction of the net force acting on you?
c. What exerts the force on you?
Thanks to Earth’s daily rotation, you always move with uniform circular motion. What
supplies the force that accelerates you? How does this motion affect your apparent
weight, that is, how would your weight be affected if the Earth stopped rotating?
A 13-gram rubber stopper is attached to a string, making a horizontal circle of radius
0.93-m. The stopper makes one revolution in 1.18 seconds. Find the tension exerted by
the string on the stopper.
Racing on a flat track, a car going 32 m/s rounds a curve 56 m in radius.
a. What is the car’s centripetal acceleration?
b. What minimum coefficient of static friction between the tires and the road would
be needed for the car to round the curve without slipping?
Early skeptics of the idea of a rotating Earth said that the fast spin would throw people
off at the equator into space. The radius of the Earth is about 6.37 x 106 m. Show why
this objection is wrong by calculating:
a. the speed of a 97-kg person at the equator
b. the force needed to accelerate the person in the circle
c. the weight of the person
d. the normal force of earth on the person, that is, the person’s apparent weight
The carnival ride shown to the right has a radius of 2.0 m
and rotates once each 0.90 seconds.
a. Find the speed of the rider
b. Find the centripetal acceleration of the rider
c. What produces this acceleration?
d. How does the rider interpret this acceleration?
e. Is the ride spinning fast enough to safely get
completely vertical?
f. What is the coefficient of static friction between the
riders and the walls if the floor could be dropped out
when the ride is perfectly horizontal?
A 65-kg circus carnie is sitting on a steadily-rotating Ferris wheel with a radius of
5.5 meters. The standard 5 minute ride gives the rider 12 full trips around the
circle.
a.
b.
c.
d.
What is the carnie’s apparent weight at the top of the ride?
What is the carnie’s apparent weight at the bottom of the ride?
What is the carnie’s apparent weight at the middle of the ride?
How fast would the ride have to rotate to give the carnie a weightless
feeling at the top of the ride?
In 1665, at the age of 23, Isaac Newton showed that ______________, the force
that makes apples fall to the Earth, is the same force that makes the moon orbit
the Earth. Not only does Earth attract apples and moons, but every body in the
universe attracts every other body. This tendency of bodies to move toward each
other is called ______________________.
Quantitatively, Newton proposed a force law that we now call Newton’s Law of
Universal Gravitation: every particle attracts every other particle with a
gravitational force whose magnitude is given by:
Here, G is the ________________ ________________________
________________. Its value is now known to be _______________________.
The direction of the gravitational force is directed toward the center of
____________________________________________.
Using this important equation, Henry Cavendish “______________” the Earth in
1798. He set up an experiment in which he used the small gravitational attraction
between two large spheres to twist a delicate wire a small amount. From this
twisting, Cavendish was able to fill in everything but the G in Newton’s equation.
Once he calculated G, Cavendish was able to determine the mass of the Earth!
A satellite orbits Earth 225 km above its surface. What is its speed in orbit and its
period?
The sun is considered to be a satellite of our galaxy, the Milky Way. The sun
revolves around the center of the galaxy with a radius of 2.2 x 1020 m. The period
of one revolution is 2.5 x 108 years.
a. Find the mass of the galaxy.
b. Assuming the average star in the galaxy has the same mass as the sun, find
the number of stars.
c. Find the speed of which the sun moves around the center of the galaxy.
Friction provides the force needed for a car to travel around a flat, circular track. What is
the maximum speed at which a car can safely travel if the radius of the track is 80.0 m
and the coefficient of friction is 0.40?
A banked curve uses normal force to get a car around a turn rather than relying solely on
friction. If a curve with radius of 30 m is banked at an angle of 42º, for what speed is this
curve rated?
ANSWERS
constant (fixed)
constant
uniform circular motion
accelerating
center
centripetal
center-seeking
net force
centripetal
name
centrifugal
illusion
directly
square
inversely
ac = v2/r
mass
period
seconds
frequency
one second
hertz
reciprocals
angular velocity
central
vertex
ω
radians
second
The force is toward the center of the tub.
The walls of the tub exert the force on the
clothes. Of course, the whole point is that
some of the water in the clothes goes out
through the holes in the wall of the tub
moving toward the center.
a. Your body is accelerated to the right.
b. The net force acting on your body is to
the right.
c. The force exerted by the car’s seat and
maybe the door to your left.
Earth’s gravity supplies the force that
accelerates you in circular motion. Your
uniform circular motion decreases your
apparent weight.
0.37 N @ 20° (.36 Rad) above horizontal
18 m/s/s
1.8
465 m/s
3.3 N
950.6 N
947.3
14m/s
97.5m/s/s
Normal Force of Walls
As a centrifugal force pushing them outward
Yes, 4.4 m/s/s < 14 m/s/s
.10
614.4 N
659.5 N
637.0 N
7.34 m/s
gravity
gravitation
Fg = m1m2/r2
Universal Gravitation Constant
6.67 x 10-11 N kg2/m2
the object exerting the gravitational force
“weighed”
7780 m/s
88.8 minutes
1.0 x 1041kg
5.0 x 1010
6.1 x 105km/h
18 m/s
16 m/s (≈ 36 mph)