OBJECTIVE: I will be able to recognize (once again) the importance of using ENERGY considerations in problem solving during today's class.

WORDS FOR TODAY:

Moment of Inertia: A measure of how much an object will resist rotation about a specific axis of rotation

Torque: Force through a displacement (NOT WORK!)

FORMULAE OBJECTUS:

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There are a veritable FLOOD of new terms to get comfortable with in this unit... so let's start NOW:

Linear & Rotational Formulae

WORK O' THE DAY: 

This unit can be a bit overwhelming due to the sheet number of formulae that we have to keep track of, let alone their linear counter parts.

Take a look at the APC Equation Sheets I passed out... Our author pretty much snows us under with equations in this unit. Notice how many of them you need to know:

10.24 (Kinetic Energy/Rotation)

10.25 (Work/Rotation) be prepared to play around with those (I'll model)

10.31 (KE of a rolling object)

 

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To Wit:

Rotational KE is pretty straightforward:

KE_R = 1/2Iω²

Notice the form is so similar to our linear analog as to be easily remembered:

KE_L = 1/2mv²

Sometime when we learn a new unit, we often forget lessons learned from previous units... remember what a pain-in-the-behind-butt-quarters it was to do 2 dimensional motion problems, and how much EASIER it was to do them using energy considerations?

Let's jump ahead to the worked problem on 10.11:

Notice how much work it takes to do this using non-energy considerations (I thought it'd be fun to try-- so I'm a nerd...)

Notice HOW MUCH Easier that same problem is using energy concerns (notice that we mix and match linear type equations with rotational equations for energy as needed)

W = ∫τdθ

Take a look on your equation sheets.... which form of these are present there?

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Now let's go back and work through example 10.10 on page 312

We've glanced at this, but go through 10.11 on page 314

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Let's check the calendar

Coursework: #45, #47 -- Careful this won't work with linear equations (the lever arm has zero mass!)... assume that when the trebuchet is launched that the heavy end falls straight down and there is zero distance between it and the ground)

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ANSWERS:

ACK! I've gotta goof in here somewhere, but I gotta run. I'll try to fix it tomorrow. In the meantime, see if you can find it (the method is fine)