Rotational Motion - PowerPoint PPT Presentation

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Rotational Motion

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Rotational Motion Angular Acceleration ... r Dq Rotational Work-Energy The net work done by forces on an object equals the change in kinetic energy. – PowerPoint PPT presentation

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Title: Rotational Motion


1
Rotational Motion
2
Angular Acceleration
  • In uniform circular motion there is a constant
    radial acceleration.
  • ar v2 / r rw2
  • If the angular velocity changes there is
    acceleration tangent to the circle as well as
    radially.

The angular acceleration is a
3
The Effect of Torque
  • A tangential force on a mass creates an
    acceleration.
  • Tangential force Ft m at
  • Tangential acceleration at ra
  • The force is associated with a torque.
  • Torque t r Ft

Ft
r
m
4
Rotational Law of Acceleration
  • The force law can be combined with rotational
    motion.
  • Torque t r Ft r m at m r2 a
  • If torque replaces force, and angular
    acceleration replaces acceleration, this looks
    like the law of acceleration.

5
Torque and Work
  • A force does work on an object acting over a
    distance.
  • A torque does work on an object rotating through
    an angle.

r
Dq
6
Rotational Work-Energy
  • The net work done by forces on an object equals
    the change in kinetic energy.
  • The net work done by torques on an object equals
    the change in rotational kinetic energy.

7
Rotational Power
  • As with translational motion, power is the rate
    of work done.
  • The earth is slowing due to the tides.
  • About 28 s / century
  • 1 part in 108
  • The kinetic energy is changing.
  • The power dissipation is large
  • About 7 billion hp

8
Rotation and Translation
  • A rolling wheel is moving forward with kinetic
    energy.
  • The velocity is measured at the center of mass.
  • KCM ½ m v2
  • A rolling wheel is rotating with kinetic energy.
  • The axis of rotation is at the center of mass.
  • Krot ½ I w2

w
v
9
Rolling Energy
  • The energy of a rolling wheel is due to both the
    translation and rotation.
  • The velocity is linked to the angular velocity.
  • The effective energy is the same as a wheel
    rotating about a point on its edge.
  • Parallel axis theorem

10
Energy Conserved
  • A change in kinetic energy is due to work done on
    the wheel.
  • Work is from a force
  • Force acts as a torque
  • Rolling down an incline the force is from
    gravity.
  • Pivot at the point of contact
  • The potential energy is converted to kinetic
    energy.

v
R
F mg
q
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