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Circular Motion
AP Physics 1
Uniform Circular Motion
Uniform Circular Motion
 Uniform circular motion describes an object
that travels along a circular trajectory at a
constant speed.
 The velocity of the object is always tangent to
the trajectory of the object.
 The magnitude of the velocity for uniform
circular motion is defined using the
circumference of the path and the period.
 Period (T) is the amount of time required to
travel once around the circle.
Centripetal Acceleration
 Although the speed of the object is constant, the
velocity is not; it is always changing direction.
 Because the velocity is changing, the object is
accelerating!
 The acceleration for uniform circular motion
points towards the center of the circle, it is
referred to as centripetal acceleration.
Forces and Circular Motion
Centripetal Force
 A particle of mass m moving at constant speed v
around a circle of radius r must always have a net force
of magnitude mv2/r pointing toward the center of the
circle.
 This is not a new kind of force: The net force is due to
one or more of our familiar forces such as tension,
friction, or the normal force.
 Centripetal force does not go on an FBD!
Example
An ice hockey puck is tied by a string
to a stake in the ice. The puck is then
swung in a circle. What force is
producing the centripetal acceleration
of the puck?
Example
A coin sits on a turntable as the table steadily
rotates counterclockwise. What force or forces
act in the plane of the turntable?
Example
What is the maximum speed with which a
1500 kg car can make a turn around a curve
of radius 20 m on a level (unbanked) road
without sliding? Assume the coefficient of
static friction is 1.0.
Centrifugal Force
 If you are a passenger in a car that turns a
corner quickly, it is the force of the car door,
pushing inward toward the center of the curve,
that causes you to turn the corner.
 What you feel is your body trying to move
ahead in a straight line as outside forces (the
door) act to turn you in a circle.
 A centrifugal force will never appear on a freebody diagram and never be included in
Newton’s laws. Because its not real. At all.
Non-Uniform Circular
Motion: Vertical Circles
Non-Uniform Circular Motion
 If an object moves in a vertical circle, the motion is not
uniform (speed is not constant).
 In this course, we will only analyze motion at the top
and bottom of a vertical loop.
 We can use this to analyze the “weirdness” experienced
while moving through a roller coaster loop.
 As you move through a vertical loop, you feel strange
effects at the top and the bottom.
 Apparent weight (how heavy you feel) is the normal
force provided by the track.
 The normal force is larger at the bottom than the top,
which is why you feel heavier at the bottom of the
track.
Critical Speed
 For an object moving in a vertical circle,
there is a minimum speed it must have to
not fall off the track.
 This minimum speed occurs when the
normal force is equal to 0.
 If the normal force equals 0, the cart is no
longer in contact with the track.
𝑚𝑣 2
𝑚𝑣 2
𝐹𝑐 =
→ 𝑁 + 𝑚𝑔 =
𝑟
𝑟
𝑁=0
𝑚𝑣 2
𝑚𝑔 =
→ 𝑣𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = 𝑟𝑔
𝑟
Example
A physics textbook swings back and forth as a pendulum.
Which is the correct free-body diagram when the book is at
the bottom and moving to the right?
Example
A person drives over a circular hill. Determine
whether the force of gravity or the normal
force on the car is larger.
The Gravitron
 The Gravitron is a fun application of
circular motion. This carnival ride spins
fast enough that the riders appear to
defy gravity.
 As the ride speeds up, the normal force
on the rider increases, which in turn
increases the force of friction acting on
the rider.
 If this frictional force is large enough, it
will perfectly cancel out the force of
gravity!