Lecture series for Conceptual Physics 8th Ed.

Rotational Inertia p118

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.

Alias: momentum of inertia.

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

Fig 7.5 Rotational inertias of some shapes:

Why does disk beat hoop down ramp?

Torque p121Torque = lever arm x force

fulcrum

mg

force

At equilibrium: CCW torque = CW torque

Torque = “la” x F =F x d

Huh?

Fl x dl = Fr x dr

300 x dl=500 x 1.5 dl=2.5m

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 white dot marks the CM of the adjustable wrench.

The CM goes straight!

Center of Gravity is basically the same as CM.

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?

Stability p125

Equilibrium exist when your CG is over your

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?

support.

More Stability

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

This one?No

This one? Yes What contributes to its greater torque?

Longer lever arm

More mass (force).

Peter Parker fooling around.

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.

Loose mud flies off on a tangent.

5g + 1g

5g – 1g

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?”

Centrifugal Force in a Rotating Frame p130

You are lighter at the equator.

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

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

?

Simulated Gravity p 131

A force toward the center.

The action force

The reaction 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.

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.)

=v / r So, L = mr2 vr = mvr

Given:

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

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

Conservation of Angular Momentum p134

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

A gymnast balls up to increase his spin rate.

The end