It’s time to anchor these It’s time to anchor these concepts we have been concepts we have been

talking about.talking about.

Translational (linear) motion

Rotational (circular) motion

Today we shall cover:Today we shall cover:

Moment of Inertia (Moment of Inertia (II)) How How I I relates to Newton’s 1relates to Newton’s 1stst law law Rotational EquilibriumRotational Equilibrium How torque relates to Newton’s 2How torque relates to Newton’s 2ndnd law law Angular MomentumAngular Momentum

The comparison begins…The comparison begins…

Rotational Motion: Rotational Motion: Moment of Inertia = Moment of Inertia = resistance to a resistance to a change in motionchange in motion

Has to do with mass Has to do with mass and where that mass and where that mass is placed in relation is placed in relation to the axisto the axis

Translational Motion: Translational Motion: Inertia = resistance to Inertia = resistance to a change in motion. a change in motion.

Has to do with Has to do with mass.mass.

Rotational Inertia (Rotational Inertia (II))(moment of inertia)(moment of inertia)

Rotational inertia: how much an object resists a Rotational inertia: how much an object resists a change in rotational motion.change in rotational motion.

I resist a change in rotational motion! Bring your torque baby!

I resist a change in rotational motion too!

Not as much as me!

It depends not only on the mass of the object, but where It depends not only on the mass of the object, but where the mass is relative to the hinge or axis of rotation – the mass is relative to the hinge or axis of rotation – which shape has the greatest moment of inertia? Why?which shape has the greatest moment of inertia? Why?

Big rotationalinertia

Small rotationalinertia

Same torque,different

rotational inertia

spinsslow

spinsfast

rotational inertia examplesrotational inertia examples

Rods of equal mass and length

axis through center

axis through end

Rotational inertia of 1 kg•m

Rotational inertia of 4 kg•m

I = 1/12 mass x length

I = 1/3 mass x length

Why would this part of physics be important to someone like little Aidan?

Summarize…Summarize…

What two things influence rotational What two things influence rotational inertia?inertia?

Look at your sheet…which has the greater Look at your sheet…which has the greater effect?effect?

Rotational EquilibriumRotational Equilibrium

ττ clockwise = clockwise = ττ counterclockwise counterclockwise How else could we express this?How else could we express this?

This means that the object is not rotating…but This means that the object is not rotating…but could it still be moving?could it still be moving?

=

EquilibriumEquilibriumTranslationalTranslational vs vs RotationalRotational

TRANSLATIONALTRANSLATIONALΣΣF = 0F = 0

Meaning:Meaning:

The net force The net force on an object on an object must be zeromust be zero

ROTATIONALROTATIONAL ΣΣττ = 0 = 0

Meaning:Meaning:

The net torque The net torque on an object on an object must be zeromust be zero

A uniform 40.0 N board supports three children. One A uniform 40.0 N board supports three children. One weighing 510 N sits 1.50 m to the right of the fulcrum, which weighing 510 N sits 1.50 m to the right of the fulcrum, which is located at the center of the board. Another kid weighs 350 is located at the center of the board. Another kid weighs 350 N is sitting 2.00 m to the right of the fulcrum. N is sitting 2.00 m to the right of the fulcrum. a. a. Where should the third child who weighs 450 N sit to Where should the third child who weighs 450 N sit to balance the system?balance the system?b. b. How much force does the support exert on the board?How much force does the support exert on the board?

fulcrum 510 N at 1.50 m.

350 N at 2.00 m

450 N at ???

40 N ‘board’

Ol’ Newton Numero dos!Ol’ Newton Numero dos!

Translational Motion:Translational Motion:

FFnetnet = ma = ma

Net force equals mass Net force equals mass times acceleration.times acceleration.

Rotational Motion:Rotational Motion:

ττnetnet = I = Iαα

Net torque equals Net torque equals moment of inertia moment of inertia times the angular times the angular acceleration.acceleration.

NEWTON’S SECOND LAW FOR NEWTON’S SECOND LAW FOR ROTATING OBJECTSROTATING OBJECTS

ττnetnet = I = Iαα

For rotational For rotational motion motion ONLYONLY

Counterclockwise = positive

Clockwise = negative

REMEMBER!!!REMEMBER!!! WHEN THE NET TORQUE IS WHEN THE NET TORQUE IS

0 THEN THE WHEEL 0 THEN THE WHEEL COULD BE AT REST OR COULD BE AT REST OR ROTATING WITH A ROTATING WITH A CONSTANT VELOCITYCONSTANT VELOCITY

Mr. Conley, can we do a lab to tie all

this together?

Oh ya I think that would be a good idea

Angular MomentumAngular Momentum

If an object has rotational inertia it also If an object has rotational inertia it also has ???????? Think about this one…if it is has ???????? Think about this one…if it is moving, it has to have….moving, it has to have….

L = IL = IωωAngular momentum =moment of inertia x angular speedAngular momentum =moment of inertia x angular speed

Untis of angular momentumUntis of angular momentum

Kg·mKg·m22/s/s

Momentum Momentum TranslationalTranslational vs.vs. angular angular

TranslationalTranslational p = mvp = mv

Momentum = mass x Momentum = mass x

speedspeed

RotationalRotational L = IL = Iωω

Rotational momentum = Rotational momentum = moment of inertia x moment of inertia x angular speedangular speed

Conservation of angular Conservation of angular momentummomentum

Angular momentum doesn’t change if Angular momentum doesn’t change if τ = 0Conservation of momentum

Watch for the concepts…Watch for the concepts…

Let’s analyze the 80’s again!More 80’s Skating!

And another random guy going for it!