Circular Motion
 Rotations and Revolutions
 Axis: straight line about which rotation takes place.
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If axis is located within the body, the motion is called a
rotation. Ex. Earth rotates and we have days
If object turns about an external axis, the rotational motion is
called a revolution. Ex. Earth revolves around the sun.
 Rotational speed
 Linear speed: is greater on the outside of a rotating
object than closer to its axis.
 Linear speed of something moving
in a circle is tangential speed.
 Rotational speed: refers to the
number of rotations or revolutions
per unit of time.
 Expressed in revolutions per minute (RPM)
 Linear speed increases as rotational speed increases and
depends on the distance from the center.
 All parts for example in a merry go round have the same
rotational speed but different linear speed.
 Centripetal force: any force that causes and object to
follow a circular path.
 Without this force, the occupants inside a rotating
carnival ride would have a straight line motion.
 Centrifugal forces
 Centrifugal force: a force “away from the center”
 It is useful only in a rotating frame of reference.
 The only force that keeps an object moving in a
circular path is the centripetal force.
 In a rotating frame of reference, centrifugal force
appears as real as the pull of gravity. But is not a true
force because it is an effect of rotation and not the
interaction between two masses.
 Simulated gravity
 Gravity is simulated by centrifugal force.
 YouTube - conceptual physics Centripital force
 In the future, we will likely life in huge lazily rotating
space stations where centrifugal forces simulate gravity.
 Right now, astronauts feel weightless because they lack a
support force.
 To simulate normal Earth gravity at 1 RPM require a
structure almost 2km in diameter and people have
difficulty adjusting to RPM greater than 2 or 3 RPMs.
 Formulas
 Period(T): the time it takes for one full rotation or
revolution of an object. (unit: second)
 Frequency(f): the number of rotations or revolution per
unit of time. Unit: 1/second or Hertz (Hz)
T= 1
f= 1
f
T
 For an object that spins in a circle, the distance it travels
in one revolution is 2r
 Tangential velocity (v) v= 2r
T
 Centripetal acceleration :ac=v2/r
 Centripetal force: Fc=mac=mv2
r
 Ex.1 If Karen spins on her chair with a frequency of
0.5Hz, what is her period?
 Ex.2 Silvia’s favorite ride at the fair is the rotor, which
has a radius of 4.0m. The ride takes 2.0s to make one
full revolution.
a. What is Silvia’s tangential velocity?
b. What is her centripetal acceleration?
 Ex. 3 Captain Ramos, the pilot of a 60500kg plane, is
told that he must remain over the airport until it is his
turn to land. If Captain Ramos flies his plane in a
circle whose radius is 50.0km once every 30.0min,
what centripetal force must the air exert against the
wings to keep the plane moving in a circle?
Circular Motion