Notes over Circular Motion
What is circular motion? The motion of things that are traveling in a circle. Notice that this is
similar to projectile motion but instead of a semi-circle, we are now working with full circles.
When objects travel in a circle there is always an axis that they travel about (around).
Axis: A straight line around which circular motion takes place
There are 2 types of circular motion Rotation and Revolution.
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Rotation: When an object turns about an “internal” axis (an axis located within the body of
the object), also called spin
Examples: Figure skater doing spins, a football spiraling, the earth on it’s axis, the platform of
a carousel
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Revolution: when an object turns around an “external” axis (an axis not necessarily connected
to the body)
Examples: the earth around the sun, the horses on the carousel,
Clearly, when objects are moving, they have a speed. There are two ways that we can measure the
speed of an object in circular motion.
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Rotational Speed (Angular Speed): number of rotations per unit of time
It is expressed in revolutions per minute RPM
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Tangential Speed: is directly proportional to rotational speed and the distance from the axis
(kinda like “regular” speed)
What causes something to move or accelerate? A force
The force that causes circular motion is called a centripetal force.
Centripetal Force: any force that causes a body to move in a circular path or in part of a
circular path, such as rounding a corner
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The only force exerted on an object moving in a circular path is directed toward the center of
circular motion
There is another term you may have heard called Centrifugal Force.
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Centrifugal Force: name given to a outward-acting force, and it is useful only in a rotating
system
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It is different from a real force in that there is no interaction (pair of forces), there is no mass
out there pulling on it
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There is no reaction counterpart to the centrifugal force that is felt, therefore it is not a real
force
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Fc (Centripetal Force)
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ac (centripetal acceleration)
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What do you think these mean?
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Basically that the object is moving with circular motion but still accelerating and still has a
force keeping it moving.
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New formulas for your Formula Sheet
Quantity
Unit
Formula
Centripetal Force
N
Fc = mac
2
Centripetal Acceleration m/s
ac= v2/r
r is the radius of the circle
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Example:
A 0.25 kg mass is attached to a 1.00 m length of string. The mass is moving in a horizontal
circle at a speed of 15.0 m/s. What is the centripetal force acting on the mass? How much
acceleration does the object have?