Transcript Circular Motion - Tenafly Public Schools

Circular Motion
Physics
Mrs Coyle
•Earth rotates about its axis
•Satellite revolves about the
earth
Part I-Intro to Circular Motion




Tangential Speed and Velocity
Frequency and Period
Centripetal Force
Centripetal Acceleration
Characteristics of Circular
Motion



Tangential (linear) Velocity
Frequency
Period
Frequency, f :
#revolutions per unit time

f = # rev / time
Units:
 (1/sec)=sec-1=Hertz (Hz)
 rpm (#rev/min)
 rps (#rev/sec)
r
Period

Period T : time for 1 revolution


Unit: sec, min, h
Relating Frequency and period

f= 1
T
Arc Length

Arc Length s (unit: meter)

Distance traveled along a circular path.
s
Average Tangential (Linear) Speed
v= s
t
v= 2pr/T = 2prf
Unit: m/s
Uniform Circular Motion

Linear(tangential speed is constant)

v=constant
Tangential (Linear) Velocity
The tangential velocity vector is
tangent to the circle at the point of
v
study.
v
Problem 1
A biker travels once around a circular
track of radius 20.0m in 3s.
Calculate:
a)
the average tangential speed
b)
the frequency
c)
the period
Answers: 41.9m/s, f=0.33Hz, T=3s
Record Player
Problem 2
A coin sits 0.10m from the center of a
record player spinning at 45rpm.
a)
What is the frequency in Hertz?
b)
What is the period?
c)
What is the linear speed?
Answer: 0.75Hz, 1.33s, 0.47m/s
Merry-go-Round
How does the v vary with r?
The linear speed increases as r increases.
Example:
 How does your linear speed change when
you are on a merry-go-round and you
move away from the center?

How does the f vary with r?

f does not depend on r
Example:
 How does your frequency change when
you are on a merry-go-round and you
move away from the center?
Centripetal Force, Fc= m v2
r



Is a center seeking force. (Always points
to the center.)
Is perpendicular to the tangential velocity
at any given instant.
It is not an extra force. An existing force
represents the centripetal force.
What forces represent the
centripetal force in these examples?




Car on bend of road.
Coin on record player.
Child on merry-go-round.
Ball tied on a string.
Centripetal Acceleration, ac= v2
r


Has same direction as centripetal
force.(Always points to the center).
Is perpendicular to the tangential
velocity at any given instant.
Centripetal Force
Fc=mac
Problem 3
A child on a merry-go-round sits 1.5m
from the center. They spin 3 times in one
min. The mass of the child is 40kg.
Find the friction(centripetal force) acting on
the child.
Answer: 5.9N
Part II
More Centripetal Force
Problems



Car Rounding a Curve
Loop-the- loop
Rotor
What force plays the role of the
centripetal force when a car
rounds a curve?
Car Rounding a Bend
Example 1: Car Rounding a
Curve


A car is travelling with a speed of 45km/h
on a circular horizontal track of radius
50m. What is the minimum coefficient of
friction, so that the car stays on the
track?
Answer: 0.3
What force plays the role of the
centripetal force when a ball is on
the top of a loop-the-loop?
Loop the Loop
Example 2: Loop-the-loop


What is the critical velocity of a ball at
the top of the loop of radius .3m so that
it completes the loop?
Answer: 1.7m/s
Rotor Ride
Rotor Ride

http://www.youtube.com/watch?v=J7k8Oz
_73mw&feature=player_embedded#
What force plays the role of the
centripetal force in the rotor ride?

http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG
Example 3: Rotor

A brave student rides in a rotor of radius 5m
whose floor drops when it reaches a speed
of 20mi/h. What is the coefficient of friction
between the student and the wall of the
rotor, so that the student does not fall?
Answer: 0.6
Recap