Rotational Motion

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

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

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.

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

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.

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

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

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

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