Rotation Notice that all the points turn through the same angle, but they travel different distances. What determines how far each point travels?

Rotation d R Θ Θ is called the angular displacement. It is measured in radians

Angular Displacement d r Θ Θ is called the angular displacement. It is measured in radians.

Angular Displacement d r Θ So the distance traveled depends on the angle of rotation and the distance from the centre

For one rotation: d = circumference = 2πr So one rotation = = 2π radians

angular speed is a measure of how quickly something turns All three spots on the wheel have different linear speeds, but they have the same angular speed.

The linear speed is given by What is the formula for speed of rotation?

The angular speed is given by Estimate the angular speed of the disc

The skater rotates 3 times in 5.0 s. Calculate her angular velocity

How does linear velocity relate to angular velocity? The blue and red spots have the same angular velocity but the blue one has a ………………… linear velocity. θ r

Angular Acceleration Linear acceleration: Angular acceleration:

Review

Review Linear/Rotation

extension

Torque Torque is the turning effect of a force. A torque produces angular acceleration Like a force produces acceleration

Force produce no torque Angular acceleration = zero Force produces a torque This causes angular acceleration

What happens in each case???

Linear acceleration is Angular acceleration is I is the rotational inertia. Newton’s Second Law (Rotation)

Inertia is a measure of how hard it is to make an object accelerate. Billy is 100kg. He is twice as hard to accelerate as Mary who is 50 kg. F F

Rotational Inertia is a measure of how hard it is to give an object angular acceleration. The car wheel has more rotational inertia than the cycle wheel

Rotational Inertia depends on: 1) The mass 2) The mass distribution. The further the mass is from the centre, the greater the rotational inertia. (harder to spin)

Changing the rotational inertia of a torsional pendulum

Which wheel (same mass, radius) has most rotational inertia?

Which wheel has most angular acceleration?

Give two advantages of carrying the pole

Why would you want wheels with a small rotational inertia?

Rotational Inertia Equations. The simplest shape to calculate is a hollow ring. Mass = m radius= r

r F

Solid Disc A solid disc is trickier because all the bits are different distances from the centre. It can be thought of as a large number of hollow rings varying from radius = 0 to radius = r. The total is

Angular Momentum Recall: linear momentum is how hard it is to stop something that’s moving. Angular momentum is how hard it is to stop something that’s spinning.

angular momentum is a VECTOR

What is the total angular momentum?

Angular Momentum of a point mass m v r

Conservation of Angular Momentum Linear momentum is constant if…… no net outside force Angular Momentum is constant if…… no net outside torque

This is a conical pendulum from below. Is angular momentum conserved? is mv 1 r 1 = mv 2 r 2 ?

This is a conical pendulum from below. Does the centripetal force cause a torque?

When she pulls her arms in, no outside torque so angular momentum is conserved. Her mass moves closer to centre so Rotational Inertia decreases. So angular velocity must increase

Minimum rotational inertia Maximum angular velocity Maximum rotational inertia Minimum angular velocity

Helicopters Why doesn’t the body turn opposite to the rotor??

Blades angular momentum Body tries to rotate Force on tail rotor Force on the spinning tail rotor causes a torque to oppose the rotation of the body

Rotational Kinetic Energy A wheel requires WORK to make it spin. A spinning wheel can push something and make it move. This means it must have energy

The equation for linear kinetic energy is…… The equation for rotational kinetic energy is…… Rotational Kinetic Energy

Which wins the race, the car (freewheeling) or the wheel?

All the car’s gravitational energy goes into translational kinetic energy (almost). Some of the ball’s gravitational energy goes into translational kinetic energy and some goes into rotational kinetic energy. So the ball has less translational kinetic energy So the ball has less velocity

For the Car GPETKERKE For the Wheel GPETKERKE

A Flywheel Bus The spinning flywheel stores Rotational Kinetic Energy when the bus brakes or goes down hill. It uses it to give the bus Translational Kinetic Energy.