Download Circular Motion Circular Motion

Circular Motion
Circular Motion:
The direction of V keeps changing,
even though the speed stays constant.
Uniform Circular Motion
• Motion at constant speed around a circle
with a fixed radius
2r
v
T
• v = velocity in a circle (m/s)
• r = radius of the circle (m)
• T = period (sec/revolution)
Period (T)
• Sometimes information may be given in RPM
(revolutions per minute)
– Be sure you convert this to seconds/revolution
– You will have to flip the number and then convert
from minutes to seconds
• Ex: The tachometer in your car reads 5000
RPM. What is the period?
1 min
 60 sec  0.012 sec/ rev
5000revolutions
Sample Problem
• A rubber stopper on the end of a 0.5m long
string completes 10 circles in 5 seconds. What
is the velocity of the rubber stopper?
2r
v
T
2 (.5m)
 6.28m/s
(5 sec/ 10rev)
Centripetal Acceleration
• Acceleration is a change in speed or direction.
• Since an object moving in a circle is constantly
changing direction, it is constantly accelerating!
• What is the centripetal acceleration for the stopper in
our example before?
ac 
2
v
r
2
(6.28 m/s)
2
 78.9 m/s
0.5 m
Centripetal Force
• The NET FORCE that causes an object to
move in a circle
• Points toward the CENTER of the circle!
• Types include:
– Gravitational Force: Planetary Motion
– Tension: Mass on a String
– Friction: Car on a Road
Circular motion on a road:
QUESTION:
What force acts as the centripetal
force here?
Sample Problem
• A 1500 kg car rounds a corner with a
radius of 25 m. If the coefficient of friction
between the tires and the pavement is 0.5,
what is the maximum speed that the car
can take the corner?
Sample Problem
• A 100g ball on the end of a 60cm long
string is swung in a horizontal circle. What
is the maximum period of the ball if the
string will break when 100 N of tension is
placed on it?
VERTICAL CIRCLES
• You must consider what
is happening at both the
top and the bottom of the
circle
• Minimum tensions will be
at the TOP of the circle.
– The minimum tension is
ZERO.
Sample Problem
• A ball (m= 0.025kg) on the end of a 0.6m
long string will complete 10 vertical
revolutions in 6 seconds. What is the
tension in the string at the top of the circle
and at the bottom?
– Draw a FBD
– Write a Net Force Equation
– Solve
Sample Problem
• What is the minimum velocity that the ball
in the previous problem can travel to make
it around the vertical circle?
Sample Problem
• A 60 kg passenger on a roller coaster with
a loop that has a radius of 20 meters,
travels at 21m/s through the loop.
– How much normal force (how much force
does the passenger feel on their bottom) does
the passenger experience at the bottom and
top of the loop?
– What is the minimum “safe” velocity for the
roller coaster?
Sample Problem
• A 60 kg driver of a car rounds the top of a
hill which has a radius of 25 meters. How
fast would the driver need to be traveling
in order to feel weightless for that instant?
– Hint: Normal force will = 0!