# 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
• ar v2 / r rw2
• If the angular velocity changes there is
acceleration tangent to the circle as well as

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

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