Download Circular motion

Circular Motion
Circular Motion
Circular motion occurs when a force causes
an object to curve in a full circle. The planets
orbiting the sun, a child on a merry-go-round,
and a basketball spinning on a fingertip are
examples of circular motion. Each moves
around its axis of rotation. The basketball’s
axis runs from your finger up through the
center of the ball. The child’s axis is a vertical
line in the center of the merry-go-round. While
their motions are similar, there is a difference.
The ball’s axis is internal or inside the object.
We say an object rotates about its axis when
the axis is internal. A child on a merry-goround moves around an axis that is external or
outside him. An object revolves when it
moves around an external axis.
Quiz
Angular Speed
Angular speed When an object moves in a line, we can
measure its linear speed. Linear speed is the distance
traveled per unit of time. Angular speed is the amount an
object in circular motion spins per unit of time. Angular
speed can describe either the rate of revolving or the rate of
rotating. Circular motion is described by angular speed. The
angular speed is the rate at which something turns. The rpm,
or rotation per minute, is commonly used for angular speed.
Another common unit is angle per unit of time. There are
360 degrees in a full rotation, so one rotation per minute is
the same angular speed as 360 degrees per minute.
Linear Speed
A merry-go-round makes 18 rotations in 3
minutes. What is its angular speed in rpm?
A child sits two meters from the center of a merrygo-round. How far does she travel during one
revolution?
If the merry-go-round makes one revolution in 10
seconds, what is the child’s linear speed?
A compact disc is spinning with an angular speed
of 3.3 rotations per second. What is its angular
speed in rotations per minute (rp\m)?
A) 200 rpm
The blades on a ceiling fan spin at 60 rotations per minute.
The fan has a radius of 0.5 meters. Calculate the linear
speed of a point at the other edge of a blade in meters per
second.
3.14 m/s
The height of the London Eye is 135m.
Each rotation takes about 30 minutes.
How fast would you be moving if you
were on the London Eye?
2(3.14)(67.5)/(30min*60s) = 0.24 m/s
A compact disc has a radius of 6 centimeters.
a. What is its circumference in meters?
b. If the cd rotates 4 times per second, what is the linear speed of a point
on the outer edge of the cd? Give your answer in meters per second.
c. What is the linear speed of a point 3 centimeters from the center of the
cd? (Assume the angular speed has not changed).
a) 0.38 meter
b) 1.52 m/s
c) 0.75 m/s
A 95-kg halfback makes a turn on the
football field. The halfback sweeps out a
path that is a portion of a circle with a
radius of 12-meters. The halfback makes
a quarter of a turn around the circle in
2.1 seconds. Determine the linear speed
of the halfback.
(2*3.14*12m)/4
= 18.84 m
18.84m/2.1 s = 8.97 m/s
(He makes ¼ of a circle)
A bicycle traveled a distance of 100 meters.
The diameter of the wheel of this bicycle is
40 cm. Find the number of rotations of the
wheel.
40 cm = 0.4 m
(2*3.14*0.2 m) = 1.256 m
100 m / 1.256 m = 79.6 rotations
During their physics field trip to the amusement park, Tyler and
Maria took a rider on the Whirligig. The Whirligig ride consists
of long swings which spin in a circle at relatively high speeds. As
part of their lab, Tyler and Maria estimate that the riders travel
through a circle with a radius of 6.5 m and make one turn every
5.8 seconds. Determine the speed of the riders on the Whirligig.
A particle is moving around in a circle
of radius R = 1.5 m with a constant
speed of 2 m/s. What is the angular
velocity of the particle?
C = (2*3.14*1.5) = 9.42 m
2 m/s = 120 m per min
120/9.42 = 17.73 rpm
During the spin cycle of a washing machine, the clothes
stick to the outer wall of the barrel as it spins at a rate
as high as 1800 revolutions per minute. The radius of
the barrel is 26 cm.
Determine the speed of the clothes (in m/s) which are
located on the wall of the spin barrel.
Circular Motion WS
1.
2.
3.
4.
A) 1188 degrees/second B) 198 rpm
A) 0.38 m B) 1.52 m/s C) 0.75 m/s
Slower
A) 0.83 m B) 1.87 m C) 1205 revolutions
D) 535 revolutions
Centripetal Force
Any force that causes an object to move in a circle.
The word centripetal means center seeking. For
object's moving in circular motion, there is a net
force acting towards the center which causes the
object to seek the center.
Centripetal Force in Space
Centrifugal Force
• Centrifugal Force IS NOT A FORCE.
• It is caused by inertia giving the appearance of a
force.
Centrifuge
A machine with a rapidly rotating container that
applies centrifugal force to its contents, typically
to separate fluids of different densities (e.g.,
cream from milk) or liquids from solids.
How Do Satellites Orbit?
mass  (tangential speed)
centripetal force =
radius of circular path
2
Practice B Page 238
1.
2.
3.
4.
29.6 kg
40.0 m
40.0 N
35.0 m/s
The maximum speed with which a 945-kg car
makes a 180-degree turn is 10.0 m/s. The radius
of the circle through which the car is turning is
25.0 m. Determine the force of friction and the
coefficient of friction acting upon the car.
A 4.0 kg ball is attached to 0.7 meter
string and spun at 2.0 meters/sec. What
is the centripetal force?
A 4.0 kg ball is attached to 0.7 meter
string and spun at 2.0 meters/sec. What
is the centripetal force?
22.85 N