Download There are 2 types of acceleration

What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
There are 2 types of acceleration:
1. Linear Acceleration
2. Radial Acceleration
Linear Acceleration is:




v
Example
t
Always parallel to the direction you are traveling.
1. If it is in the same direction as velocity. The velocity increases.
Example
2. If it is in the opposite direction as velocity. The velocity decreases.
Always parallel to the path. So, it is also called Tangential Acceleration ( aT ).
Only changing the speed of the object.
What you learned about in Kinematics: a 
Radial Acceleration is:
 Always perpendicular to the direction you are traveling.
 Always changes the direction you are traveling.
 Always points toward the center of the circular path you are taking.
So, it is also called Centripetal Acceleration.
Example #1 Car going around curves
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Example #2 Planet orbiting the sun
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What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
Remember that velocity is a vector. Vectors have a magnitude and direction. For velocity this would be speed
and direction. So… aT changes the speed and ac changes the direction. Here are 2 examples that have both
tangential ( aT ) and centripetal ( ac ) acceleration.
(Luckily for us, the AP Physics B test rarely has a problem where you need to worry
about both tangential and centripetal acceleration at the same time!)
Example #1 Car going around curves while changing speed
Example #2 Ball tossed though the air
If you are only changing the direction you are going and maintain a constant speed:
You are in Uniform Circular Motion (UCM for short).
Things to remember about UCM:
 UCM is circular motion at a constant speed.
 The only acceleration there is will be centripetal acceleration.
 The centripetal acceleration always points toward the center of the circle. ALWAYS!
 Since the acceleration is toward the center on the circle the net force causing the acceleration must also
point toward the center of the circle. This net force is called the Centripetal Force because it causes the
objects to move in a circle. Remember: the Centripetal Force is ALWAYS toward the center of the circle.
 NEVER EVER use the words centrifugal force on the AP test because there is no such thing as a
centrifugal force! When you are a passenger in a car and the driver makes a hard left turn; your body wants
to continue forward in a straight line because you have mass and inertia (Newton’s 1st Law). The
door/seatbelt supplies a centripetal force and makes you move in a circular path with the car. If you don’t
believe this, take off the passenger door and don’t wear your seatbelt and let the driver turn hard left. You
will not turn left with the car! You will continue on a straight path because, there is not a force toward the
center of the circle causing you to turn left!
Chris Bruhn
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6/27/2017
What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
So…Here is the picture of Uniform Circular Motion (UCM).
Note that vT (Tangential Velocity) is
always parallel to the path and in the
direction of motion and that Fc and
ac are perpendicular to vT and
always point toward the center of the
circle.
Some form or this picture will
always show up on the test!
v2
r

To calculate the centripetal acceleration use this equation: ac 

To calculate the velocity of the object: Circumference   d  2 r  2 rf
TimePeriod
T
T
r = radius of the circle
v = tangential velocity
d = diameter
T = time period
f = Frequency

v2
To calculate Centripetal Force: Fc  mac  m
r
m = mass
Classic Trick Question: How much Work does the Centripetal Force do during one complete revolution?
Answer: There are two ways to come to the correct solution.
1. Since the Centripetal Force is always perpendicular to the velocity, and thus perpendicular to the
instantaneous direction of the displacement, Work = 0. This is because W  Fr cos , and the angle
between F & r is 90 . cos 90  0 therefore, Work = 0!
2. Remember that energy remains constant unless there is work done on the system. Since the Kinetic
and Potential energies of the object do not change in UCM, Work = 0!
So… Centripetal Forces of any kind NEVER do any work on the object!
Chris Bruhn
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What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
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



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Things to know about Centripetal Force.
Centripetal Force is not a magical new force. It is any force that causes an object to move in a circle.
The Centripetal Force can be Gravity, Tension, Normal Force, Friction, etc…
The Centripetal Force can even be a component of a force or a combination of forces!
Since we are talking about forces here, you will use  F  ma to solve for Centripetal Force.
Remember!
When you set up a Centripetal Force problem remember to:
1. Draw a Free Body Diagram & label all the forces. (NEVER label any of the forces Fc !)
2. When choosing what directions to break component of forces into, always choose the direction of
Centripetal Acceleration as one of the directions.
There are only three types of Centripetal Force problems:
1. A single force causes circular motion.
2. A component of a force causes circular motion.
3. Combinations of forces cause circular motion.
Examples of a single force that causes circular motion.
Example #1 The Earth going
Example #2 A car going
around the sun: Fc = Gravity
around a turn: Fc = Friction
Example #3 An amusement park ride:
Fc
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= Normal Force
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What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
Examples where a force component causes circular motion.
Example #4 A ball on the end of a string being spun around in a circle:
Fc
= Horizontal Component of the Tension
Example #5 Car going around a banked turn:
Fc
= Horizontal Component of the Normal Force
Chris Bruhn
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What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
Examples where several forces combine to cause circular motion.
Example #6 A ball on the end of a string being spun in a vertical circle:
Fc
= Combination of Gravity and Tension
Example #7 Can going over the top of a hill:
Fc
= Combination of Gravity and Normal
Force
Chris Bruhn
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6/27/2017
What you absolutely have to know about
Circular Motion to pass the AP Physics B test!
Last Hints and Tricks:
 Never label your Free Body Diagram with the term “Centripetal Force” or “ Fc ”. Remember that Centripetal
Force is not a magical new force. It is any force that causes an object to move in a circle. You need to label
your FBD with the actual force such as Gravity, Tension, Normal Force, Friction, etc…
 Centripetal Force ( Fc ) and Acceleration ( ac ) always point toward the center of the circular path.


Velocity ( v ) in UCM is always tangential to the path in the direction the object is traveling.
They love to include 2 Dimensional/Trajectory motion in with UCM. Remember: If the force causing the
object to move in a circle magically disappears then, the problem becomes a kinematics problem with the
initial velocity being the Tangential Velocity it had in UCM! Here are a few examples.
Example #1 Car going around a turn and hits a patch of ice.
Example #2 A ball on the end of a string being
spun in a horizontal circle and the string breaks.
Fc
= Combination of Gravity and Tension
Example #3 A ball on the end of a string being
spun in a vertical circle and the string breaks.
Chris Bruhn
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