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Circular Motion
Chapter 9
Circular Motion
• Axis – is the straight line around which
rotation takes place.
• Internal Axis - is located within the body of
the object.
Circular Motion
• Rotation – is the spin around the internal
axis.
• External axis – is outside the body of the
object.
Circular Motion
• Linear speed - is distance/time
• Since the outer edge of on object moving in
a circle moves further it has greater linear
speed.
Circular Motion
• Tangential speed – is the same as linear
speed only with a circular motion.
Circular Motion
• Rotational speed - is the # of rotations/time
• Tangential speed is approximately equal to
radial distance x rotational speed.
Circular Motion
• IN ANY RIGIDLY ROTATING SYSTEM,
ALL PARTS HAVE THE SAME
ROTATIONAL SPEED.
Circular Motion
• Period (T) is the time it takes for one full
rotation or revolution of an object.
(measured in seconds)
Circular Motion
• Frequency (f) is the # of rotations or
revolutions per unit of time. (measured in
Hertz Hz).
Circular Motion
• T = 1/f
• f = 1/T
Circular Motion
• Every object exerts gravitational force on
every other object.
• The force depends on how much mass the
objects have and on how far apart they are.
• The force is hard to detect unless at least
one of the objects has a lot of mass.
Circular Motion
• Gravity is the force that keeps planets in
orbit around the sun and governs the motion
of the rest of the solar system.
• Gravity alone holds us to the earth’s surface
and explains the phenomenon of the tides.
Reminders
• Velocity is speed and the direction of travel.
• Acceleration is the rate of change of
velocity.
• Force cause the acceleration of motion.
• Work is done on an object to change the
energy of the object.
Some definitions
• Centripetal means “center seeking”
• Centrifugal means “center fleeing”
Circular Motion
• Consider a Ferris wheel. The cars on the
rotating Ferris wheel are said to be in
circular motion.
Circular Motion
• Any object that revolves about a single axis
undergoes circular motion.
• The line about which the rotation occurs is
called the axis of rotation.
• In this case, it is a line perpendicular to the
side of the Ferris wheel and passing through
the wheel’s center.
Tangential speed
• Tangential speed (vi) can be used to
describe the speed of an object in circular
motion.
• The tangential speed of a car on the Ferris
wheel is the car’s speed along an imaginary
line drawn tangent to the car’s circular path.
Tangential speed
• This definition can be applied to an object
moving in circular motion.
• When the tangential speed is constant, the
motion is described as uniform circular
motion.
Tangential speed
• The tangential speed depends on the
distance from the object to the center of the
circular path.
Tangential speed
• For example, consider a pair of horses sideby-side on a carousel.
• Each completes one full circle in the same
time period, but the horse on the outside
covers more distance than the inside horse
does, so the outside horse has a greater
tangential speed.
Centripetal Acceleration
• Suppose a car on a Ferris wheel is moving
at a constant speed around the wheel.
• Even though the tangential speed is
constant, the car still has an acceleration.
Centripetal Acceleration
• a = vf - vi
________
tf - ti
Centripetal Acceleration
• Or put in words, centripetal acceleration is
equal to linear speed squared divided by the
radius.
Speed
• V = (2Πr) / T
Centripetal Acceleration
• Acceleration depends on a change in the
velocity.
• Because velocity is a vector, acceleration
can be produced by a change in the
magnitude of the velocity, a change in the
direction of the velocity, or both.
Centripetal Acceleration
• The acceleration of a Ferris wheel car
moving in a circular path and at constant
speed is due to a change in direction.
• An acceleration of this nature is called a
centripetal acceleration.
Centripetal Acceleration
• The magnitude of a centripetal acceleration
is given by the following equation.
• Centripetal acceleration = (tangential
speed)2 / radius of circular path
Example
• A test car moves at a constant speed around
a circular track. If the car is 48.2 meters
from the track’s center and has a centripetal
acceleration of 8.05 m/s2 what is the car’s
tangential speed?
Solution
• Given:
r = 48.2 m
ac = 8.05 m/s2
Unknown:
vt = ?
Solution
• ac = vt2 / r
• 8.05 m/s2 = vt2 / 48.2 m
• vt = 19.7 m/s