Circular Motion

1
Circular Motion

• Chapter 9

2
Circular Motion

• Axis is the straight line around which rotation
  takes place.
• Internal Axis - is located within the body of the
  object.

3
Circular Motion

• Rotation is the spin around the internal axis.
• External axis is outside the body of the object.

4
Circular Motion

• Linear speed - is distance/time
• Since the outer edge of an object moving in a
  circle moves further it has greater linear speed.

5
Circular Motion

• Tangential speed is the same as linear speed
  only with a circular motion.

6
Circular Motion

• Rotational speed - is the of rotations/time
• Tangential speed is approximately equal to radial
  distance x rotational speed.

7
Circular Motion

• IN ANY RIGIDLY ROTATING SYSTEM, ALL PARTS HAVE
  THE SAME ROTATIONAL SPEED.

8
Circular Motion

• Period (T) is the time it takes for one full
  rotation or revolution of an object. (measured in
  seconds)

9
Circular Motion

• Frequency (f) is the of rotations or
  revolutions per unit of time. (measured in Hertz
  Hz).

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Circular Motion

• T 1/f
• f 1/T

11
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.

12
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 earths surface and
  explains the phenomenon of the tides.

13
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.

14
Some definitions

• Centripetal means center seeking
• Centrifugal means center fleeing

15
Circular Motion

• Consider a Ferris wheel. The cars on the rotating
  Ferris wheel are said to be in circular motion.

16
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
  wheels center.

17
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 cars speed along an imaginary line drawn
  tangent to the cars circular path.

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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.

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Tangential speed

• The tangential speed depends on the distance from
  the object to the center of the circular path.

20
Tangential speed

• For example, consider a pair of horses
  side-by-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.

21
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.

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Centripetal Acceleration

• a vf - vi

________
tf - ti
23
Centripetal Acceleration

• Centripetal acceleration is equal to linear speed
  squared divided by the radius.

24
Speed

• V (2?r) / T

25
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.

26
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.

27
Centripetal Acceleration

• The magnitude of a centripetal acceleration is
  given by the following equation.
• Centripetal acceleration (tangential speed)2 /
  radius of circular path

28
Example

• A test car moves at a constant speed around a
  circular track. If the car is 48.2 meters from
  the tracks center and has a centripetal
  acceleration of 8.05 m/s2 what is the cars
  tangential speed?

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Solution

• Given
• r 48.2 m
• ac 8.05 m/s2
• Unknown
• vt ?

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Solution

• ac vt2 / r
• 8.05 m/s2 vt2 / 48.2 m
• vt 19.7 m/s