It’s time to anchor these concepts we have been talking about. Translational (linear) motion Rotational (circular) motion

Today we shall cover:  Moment of Inertia ( I )  How I relates to Newton’s 1 st law  Rotational Equilibrium  How torque relates to Newton’s 2 nd law  Angular Momentum

The comparison begins…  Rotational Motion: Moment of Inertia = resistance to a change in motion  Has to do with mass and where that mass is placed in relation to the axis  Translational Motion: Inertia = resistance to a change in motion.  Has to do with mass.

Rotational Inertia ( I ) (moment of inertia)  Rotational inertia: how much an object resists a 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 the mass is relative to the hinge or axis of rotation – which shape has the greatest moment of inertia? Why?

Big rotational inertia Small rotational inertia Same torque, different rotational inertia spins slow spins fast

rotational 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…  What two things influence rotational inertia? Look at your sheet…which has the greater effect?

Rotational Equilibrium  τ clockwise = τ counterclockwise  How else could we express this?  This means that the object is not rotating…but could it still be moving? =

Equilibrium Translational vs Rotational  TRANSLATIONAL ΣF = 0 ΣF = 0Meaning: The net force on an object must be zero  ROTATIONAL Στ = 0 Στ = 0Meaning: The net torque on an object must be zero

A uniform 40.0 N board supports three children. One 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 N is sitting 2.00 m to the right of the fulcrum. a. Where should the third child who weighs 450 N sit to balance the system? b. 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!  Translational Motion:  F net = ma  Net force equals mass times acceleration.  Rotational Motion:  τ net = Iα  Net torque equals moment of inertia times the angular acceleration.

NEWTON’S SECOND LAW FOR ROTATING OBJECTS  τ net = Iα  For rotational motion ONLY   Counterclockwise = positive   Clockwise = negative

REMEMBER!!! WHEN THE NET TORQUE IS 0 THEN THE WHEEL COULD BE AT REST OR ROTATING WITH A CONSTANT VELOCITY WHEN THE NET TORQUE IS 0 THEN THE WHEEL COULD BE AT REST OR ROTATING WITH A CONSTANT VELOCITY

Mr. Conley, can we do a lab to tie all this together? Oh ya I think that would be a good idea

Angular Momentum  If an object has rotational inertia it also has ???????? Think about this one…if it is moving, it has to have…. L = Iω Angular momentum =moment of inertia x angular speed Untis of angular momentum Kg·m 2 /s

Momentum Translational vs. angular  Translational p = mv p = mv Momentum = mass x speed speed  Rotational L = Iω L = Iω Rotational momentum = moment of inertia x angular speed

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

Watch for the concepts… Let’s analyze the 80’s again!More 80’s Skating! And another random guy going for it!