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Lecture series for Conceptual Physics 8 th Ed.

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Lecture series for Conceptual Physics 8 th Ed. Rotational Inertia p118. Alias: momentum of inertia. The property of an object to resist being rotated. T.R. Walker starts to fall. So, he pushes down on his right and pulls up on his left to right himself. The pole stays put.

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slide2

Rotational Inertia p118

Alias: momentum of inertia.

The property of an object to resist being rotated

T.R. Walker starts to fall.

So, he pushesdown on his right and pullsup on his left to right himself. The pole stays put.

Whose legs have the least rotational inertia in fig. 7.3?

slide3

Fig 7.5 Rotational inertias of some shapes:

Why does disk beat hoop down ramp?

slide4

Torque p121

Torque = lever arm x force

fulcrum

force

mg

At equilibrium: CCW torque = CW torque

slide5

Fl x dl = Fr x dr 300 x dl=500 x 1.5 dl=2.5m

Torque = “la” x F =F x d

Huh?

slide6

Center of Mass and Center of Gravity p123

Fig 7.11 shows the ball following a smooth parabola and the bat wobbling.

In both cases, the CM makes a smooth parabola.

The white dot marks the CM of the adjustable wrench.

The CM goes straight!

Center of Gravity is basically the same as CM.

slide7

Locating the Center of Gravity p 124

Tccw = Tcw

NOTE: The weight of the stick acts at its center of gravity.

For weird shapes:

For athletes:

Which one is more stable?

slide8

Stability p125

Equilibrium exist when your CG is over your

support.

Whoops!

The amount of stability is determined by how high the CG must be raised in order to tip the object over.

Most stable

U=mgh?

slide9

More Stability

In fig. 7.24 which has the greater torque around the imaginary fulcrum?

No

This one?

What contributes to its greater torque?

Yes

This one?

Longer lever arm

More mass (force).

Peter Parker fooling around.

slide10

Centripetal Force p128

The force on a moving object that is directed towards a fixed center.

Is the water forced away from the clothes?

No!

The clothes are forced away from the water.

5g – 1g

Loose mud flies off on a tangent.

5g + 1g

slide11

Centrifugal (the imaginary) force p129

When the car stops and you’re “thrown” against the dashboard, you don’t say a force pushed you forward.

You say, “My inertia kept me going and the dashboard pushed on me.”

The bug wants to go in a straight line but the can pushes it toward the center

Does the bug say, “I’m pushing on the floor?”

slide12

Centrifugal Force in a Rotating Frame p130

The silly bug still thinks that it is in a stationary can pushing on the floor.

You are lighter at the equator.

Bugs in the space tire think that they have “gravity”.

?

slide13

Simulated Gravity p 131

A force toward the center.

The reaction force

The action force

But, this is an imaginary force.

If the floor were to give way, would he fly away from the center?

NO!

He would sail off on the tangent.

slide14

Angular Momentum p133

You remember, of course, that linear momentum, p, = m x v.

Since mass and inertia are aspects of the same thing, then you wouldn’t be surprised that…

AnguLar momentum = rotational inertia x rotational velocity

L = I

(I = mr2 or I = ½ mr2, etc.)

Given:

v

=v / r

So, L = mr2

= mvr

r

What is angular momentum of the ball if m = 2kg, v = 3m/s and r = 4m?

L=mvr=(2)(3)(4)= 24kg-m2/s

slide15

Conservation of Angular Momentum p134

I

A falling cat rotates its front half to rotate the back in the other direction, then straightens out for a 4 footed landing

=

I

A gymnast balls up to increase his spin rate.

The end

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