Transcript Circular Motion - Tenafly Public Schools

Circular Motion
AP Physics
Mrs Coyle
Rotation vs Revolution
•Earth rotates about its axis
•Satellite revolves about
the earth.
Uniform Circular Motion

Linear(tangential)speed, v, is constant.
-Tangential Velocity
-Centripetal Acceleration
-The tangential
velocity vector is
tangent to the circle at
the point of study.
v= 2pr/T = 2prf = d/t
v
v
-Centripetal Acceleration: points to center
a= v2 / r
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. It is an
existing force(s) that point(s) to the
center.
What force represent s the centripetal
force for a coin on a record player?
What force plays the role of the
centripetal force when a car
rounds a curve?
Car Rounding a Bend (Flat Road)
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
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 2: 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
What forces represent the
centripetal force for a child on this
ride?
Example 3 Conical Pendulum
Find an expression
for v in terms of L
and q.
___________
Ans: v=√Lgsin q tan q

Can q be 90o for a conical pendulum?
(Can there be a horizontal circular path
when twirling a ball)?
Example 4 Car on a banked
road
At what angle should
the road be banked if a
car is to safely round
the curve at a speed of
13.4 m/s and the radius
of the curve is 50m if
friction is neglected?
Ans: 20.1o
Non-Uniform Circular Motion


v tangential is not constant.
There are both tangential and radial
accelerations and therefore forces.
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 5: 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