Download Ch 9 Notes

Name______________________________________Block_____Date________________
Ch. 9 Circular Motion Notes
Mrs. Peck
Objectives:
Distinguish between rotate and revolve 9.1
Describe the 2 types of circular motion of the Earth and the effect of these circular motions 9.1
Describe rotational speed 9.2
Give examples of centripetal force 9.3
Describe the motion of an object if the centripetal force acting on it ceases 9.4
Explain why centrifugal force is “fictitious” 9.5
Given the frequency or period of an object, determine the tangential speed, centripetal
acceleration, and centripetal force (6.1 problem solving book)
T=1
f=1
f
T
v=2πr
T
ac = v2
r
Fc = mac = mv2
r
9.1 Rotation and Revolution
axis - the straight line around which an object may rotate or revolve
rotation- the spinning motion that takes place when an object rotates about an axis located within
the object
revolution - motion of an object turning around an axis outside the object
does a tossed football rotate or revolve?
Does a ball whirled overhead at the end of a string rotate or revolve?
The Earth undergoes 2 types of circular motion: rotation and revolution
description
axis
causes
rotation
revolution
Northern Hemisphere
Northern Hemisphere
direct rays
direct rays
Sun
Southern
Hemisphere
Southern
Hemisphere
2
period- the time it takes for one full rotation or revolution
symbol - T
unit - s (second)
T=1
f
frequency - the number of rotations or revolutions per unit time
unit - s-1; hertz
symbol - f
f=1
T
period and frequency are reciprocals of each other
T=1
and
f
f=1
T
9.2 Tangential Speed
linear speed - the path distance moved per unit of time
symbol - v
tangential speed -the speed of an object moving along a circular path
v= 2 π r
T
SI unit - m/s
symbol - v
is the linear speed that is tangent to the curved path
SI unit - m/s
v
linear speed and tangential speed are the same when dealing with circular motion
linear speed = tangential speed
tangential speed increased as radius increases
(v increases as move further from center)
Linear speed varies with the distance from the axis of rotation
A distance from center is r
.
center
A
.
B
.
B distance from center is 2r
B has twice v
Linear- Tangential speed
B
(tangential speed)
>A
***center of rotating system has no tangential speed!
as A
3
period and frequency are reciprocals of each other
linear or tangential speed = distance (circumference)
time for 1 rev. (period)
T=1
f
and
f=1
T
v=2πr
T
? If Sean spins with a frequency of 6 rpm, what is the period of his spin?
? Summerly is on a ferris wheel that turns around once every 30 seconds. What is her period
when an obj. spins in a circle? (the distance it travels in one revolution is the circumference of the circle, 2πr.
The time it takes for one revolution is the period, T.) What is her tangential speed when she is seated 7m
from the axis of the ferris wheel.
? Vincent sits on a rotor ride 4 m from the center. The ride has a frequency of 0.5 Hz (the rotor ride
will make a half of a full revolution in one second) What is Vince’s tangential or linear speed?
9.2 Rotational Speed
4
rotational speed - the number of rotations or revolutions per unit of time (RPM or RPS)
angular speed - number of rotations per unit of time
symbol - w (omega) unit: RPM or RPS
rotational speed and angular speed are same for circular motion
rotational speed = angular speed
***all parts of a rotating system are rotating together
***all parts of a rotating system rotate around their axis in the same amount of time
***all parts or points on the system have the same rotational speed...same RPM
.
center
A
.
B
.
A and B rotate around the
center the same number of
revolutions per time (RPM)
Rotational speed A = Rotational speed B
wA = wB
at the center of rotating system the tangetial speed is___________________________
at the center of rotating system the rotational speed is __________________________
as you move away from center....the tangential speed___________________________
as you move away from center ....the rotational speed __________________________
Tangential speed depends on __________________ & _________________________
Tangential speed ~ rotational speed
Tangential speed ~ radial distance (dist. from axis of rotation)
5
? Which part of Earth’s surface has the greatest rotational speed about Earth’s axis?
? Which part of the Earth has the greatest linear speed relative to Earth’s axis?
? On a merry-go-round, the horses along the outer rail are located three times farther from the axis
of rotation than the horses along the inner rail. If a boy sitting on a horse near the inner rail has a
rotational speed of 4 RPM and a tangential speed of 2 m/ s, what will be the rotational speed and
tangential speed of his sister who is sitting on a horse along the outer rail?
? Trains ride on a pair of tracks. For straight-line motion, both tracks are the same length. But which
track is longer for a curve, the one on the outside or the one on the inside of the curve?
? During track and field longer sprinting events, such as the 440m dash, why do the runners begin
at staggered starting points instead of all at the same starting point as they do with shorter sprinting
events such as the 100m dash?
9.3 Centripetal Acceleration and Centripetal Force
6
centripetal acceleration - acceleration directed toward the center of the circle
change in velocity per unit of time
rate at which velocity is changing
velocity is changing bcs object is constantly changing its direction as it follows a curved path
centripetal acceleration = (linear speed)2
radius
ac = v2
symbol: ac
SI unit: m/ s2
r
if mass is being accelerated toward the center of a circle, it must be acted upon by an unbalance net force that
gives it this acceleration
? Joe is sitting 2m from the center of a merry-go-round that has a frequency of 1. 25 Hz. What is
Joe’s centripetal acceleration? What is the direction of the centripetal acceleration?
centripetal force - a center-directed force that causes an object to move in a curved path
(sometimes circular path)
symbol: Fc
SI unit: N
other unit: kg m/ s2
Fc- any force that causes a body to move in a circular path or in part of a circular path(arc)
means “center-seeking”
any force that is directed at right angle to the path of a moving object
centripetal force = (mass) (centripetal acceleration)
Fc = mac = mv2
r
? If Joe’s mass is 60 kg, then what is the centripetal force acting on him when he is on the merrygo-round in the question above?
7
? A 0.02 kg sock is spinning inside a dryer with a speed of 1.5 m/ s. If the sock is 0.5 m from the
center of the dryer, then how much centripetal force is exerted on the sock?
Centripetal Force
fig 9.5: Car going around a curve: Fc is the friction between road and tires
friction is what pulls car inward & keeps car in curved path
if friction is not large enough to keep car in curved path....car moves off at a tangent to
the curve in a straight line path (car skids)bcs of car’s inertia
fig 9.6 the tub wall exerts Fc on the clothes forcing it into a circular path, but not the water. Water
escapes bcs no Force acting on it.......so water stays in st. line path perpendicular or
tangent to curve.
Centripetal Force (Fc) is the net unbalanced force directed inward toward the center of
a circle
Centripetal Force (Fc ) is the Fnet that causes centripetal acceleration (ac)
9.4 Centripetal and Centrifugal Forces
centrifugal force - an apparent outward force on a rotating or revolving body.
it is fictitious in the sense that it is not part of an interaction but is due to the tendency of a moving
body to move in a straight-line path due to inertia
centrifugal means “center-fleeing”
BIG MISCONCEPTION: centrifugal force pulls outward on an object in a circular path
fig 9.7 then string breaks....misconception.....centrifugal force pulls can from its circular path
reality....can goes off in a straight-line path tangent to circle because
there is NO FORCE acting on can anymore
fig 9.8 only the force from the string acts on the can to pull the can inward there is no outward
force acting on the can