Rotation, angular motion & angular momentom

Physics 100

Chapt 6

Rotation

Rotation

d1

d2

The ants moved differentdistances: d1 is less than d2

Rotation

Both ants moved theSame angle: 1 = 2 (=)

Angle is a simpler quantity than distance for describing rotational motion

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle velocity v

change in delapsed time=

angular vel.

change in elapsed time=

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle

acceleration a

change in velapsed time=

angular accel.

change in elapsed time=

velocity v angular vel.

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle

acceleration a angular accel. velocity v angular vel.

Moment of inertia = mass x (moment-arm)2

mass m

resistance to change in the state of (linear) motion

Moment of Inertia I (= mr2)

resistance to change in the state of angular motion

M

x

momentarm

Moment of inertial

M Mx

r r

I Mr2

r = dist from axis of rotationI=small

I=large(same M)

easy to turnharder to turn

Moment of inertia

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle

acceleration a angular accel. velocity v angular vel.

Force F (=ma) torque (=I)

torque = force x moment-arm

Same force;bigger torque

Same force;even bigger torque

mass m moment of inertia I

Teeter-Totter

F

Fbut Boy’s moment-arm is larger..

His weight produces a

larger torque

Forces are the same..

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle

acceleration a angular accel. velocity v angular vel.

Force F (=ma) torque (=I)

mass m moment of inertia I

momentum p (=mv) angular mom. L(=I)

Angular momentumis conserved:

L=const

I = I

Conservation of angular momentum

I

I

I

High Diver

I

I

I

Conservation of angular momentum

II

Angular momentum is a vector

Right-hand rule

Conservation of angular momentum

L has no verticalcomponent

No torques possible Around vertical axisvertical component of L= const

Girl spins:net vertical

component of Lstill = 0

Turning bicycle

L

L

These compensate

Torque is also a vector

wrist bypivot pointFingers in

F direction

F

Thumb in

direction

another

right-hand ruleF

pivotpoint

is out ofthe

screen

example:

Spinning wheel

F

wheel precesses

away from viewer

Angular vs “linear” quantities

Linear quantity symb. Angular quantity symb.

distance d angle

acceleration a angular accel. velocity v angular vel.

Force F (=ma) torque (=I)

mass m moment of inertia I

momentum p (=mv)

kinetic energy ½ mv2

angular mom. L(=I)

rotational k.e. ½ I

I

V KEtot = ½ mV2 + ½ I2

Hoop disk sphere race

Hoop disk sphere race

I

I

I

Hoop disk sphere race

II

I

KE = ½ mv2 + ½ I2

KE = ½ mv2 + ½ I2

KE = ½ mv2 + ½ I2

Hoop disk sphere race

Every sphere beats every disk

& every disk beats every hoop