Simple Nature - Light and Matter

o/The geometric relationships referred to in the relationship between force and torque. was not zero total force on it, its cent ...

whereris the distance from the axis to the point of application of the force, andF⊥is the component of the force that is perpend ...

q/Visualizing torque in terms of r⊥. r/Example 7. Sometimes torque can be more neatly visualized in terms of the quantityr⊥shown ...

s/Discussion question D. t/Discussion question E. Discussion Questions A This series of discussion questions deals with past stu ...

v/The windmills are not closed systems, but angular momentum is being transferred out of them at the same rate it is transferred ...

The pole has three forces on it, each of which may also result in a torque: (1) the gravitational force, (2) the cable’s force, ...

x/Example 9. y/Stable and unstable equi- libria. z/The dancer’s equilibrium is unstable. If she didn’t con- stantly make tiny ad ...

aa/Example 10. to either side of equilibrium will increase it, whereas the unstable equilibrium represents a maximum. Note that ...

ab/Describing a curve by givingφas a function ofr. ac/Proof that the two an- gles labeledφare in fact equal: The definition of a ...

ad/Quantities referred to in the proof of part (3). momentum tells us thatL =mrvsinφis a constant. Since the planet’s mass is a ...

a/The two atoms cover the same angle in a given time interval. b/Their velocity vectors, how- ever, differ in both magnitude and ...

c/Analogies between rota- tional and linear quantities. d/We construct a coordi- nate system that coincides with the location an ...

e/Even if the rotating object has zero angular acceleration, every point on it has an ac- celeration towards the center. axis. W ...

Radial acceleration at the surface of the Earth example 14 .What is your radial acceleration due to the rotation of the earth if ...

f/Analogies between rota- tional and linear quantities. g/Example 15 is I= ∑ miri^2 , [definition of the moment of inertia; for ...

The parallel axis theorem example 16 .Generalizing the previous example, suppose we pick any axis parallel to axis 1, but offset ...

each one of them. Using the sigma notation, this becomes ∑^8 r=1 ∑^8 c=1 1. If you’re familiar with computer programming, then y ...

differential. The result is area = ∫b y=0 ∫a x=0 dA = ∫b y=0 ∫a x=0 dxdy = ∫b y=0 (∫a x=0 dx ) dy = ∫b y=0 ady =a ∫b y=0 dy =ab. ...

volume = ∫a z=0 ∫a y=0 ∫a x=0 dxdydz = ∫a z=0 ∫a y=0 adydz =a ∫a z=0 ∫a y=0 dydz =a ∫a z=0 adz =a^3 Area of a circle example 20 ...

of inertia as if the object was smooth and continuous throughout, rather than granular at the atomic level. Of course this granu ...