PHYS 211 Final Study Guide  

What are rotational dynamics?

Study guide is most useful with my notes that give highly important diagrams I will also skip useless and unimportant subchapters so you save a lot of time studying from my study guide. This study guide highlights only the important parts of my notes, so you save time​. ____________________________________________________________________________ Equations to know how to use: 

1. Fnet = ma

2. Tnet = Iα (similar to Fnet)

3. I = mr2 

4. L = Iw

5. Krot = ½mr2w2 = ½Iw2 

What is an example of static equilibrium?

6. wf = wit + αt

7. θ = wit + ½αt2 

8. wf2 = wi2 + 2αtθ

9. T = rFsin(θ)

10. Tgrav = -mgxcom 

11. Fg = (GMm)/r2 

12. Fs = usn

13. Fk = ukn

14. Fr = urn

How is angular momentum defined?

15. ac = v2/r = w2r Don't forget about the age old question of How do you calculate the weighted average cost of capital?

16. Fs = Static Friction

17. Fk = Kinetic Friction

18. Fr = Rolling Friction

19. Fg = Force of Gravity

G = Gravitational constant

T = Torque

Tgrav = Gravitational Torque (Torque caused by gravity)

I = Moment of Inertia

L = Angular Momentum

α = Angular Acceleration

w = Angular Velocity

θ = Angle

r = Radius

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Chapter 12 - Rotation of a Rigid Body: 

12.1 Rotational Motion: Don't forget about the age old question of How does territoriality become adaptive?
Don't forget about the age old question of Who own factors of production?

Rigid Body- An object whose size and shape does not change as it moves Rotational Kinematics:

1) wf = wit + αt

2) θ = wit + ½αt2 

3) wf2 = wi2 + 2αtθ

12.2 Rotation About the Center of Mass: 

Xcom = center of mass on x-axis = (m1x1 + m2x2 + m3x3 + …) / (m1 + m2 + m3 + …) Ycom = center of mass on y-axis = (m1y1 + m1y2 + m1y3 + …) / (m1 + m2 + m3 + …) 12.3 Rotational Energy: We also discuss several other topics like Where is antitragus located?

Kinetic Energy due to rotation > Rotational Kinetic Energy (pretty straightforward) Krot = ½m1r12w + ½m2r22w + ½m3r32w + …

Moment of Inertia = I = m1r12 + m2r22 + …

-Object’s I depends on the axis of rotation, because that changes the r values Krot = ½Iw2

Objects with larger moment of inertia are harder to rotate

Emech = Krot + Ug = ½Iw2 + MgycomIf you want to learn more check out What does the circular flow model demonstrate in Economics?

12.4 Calculating Moment of Inertia: We also discuss several other topics like What is the power of media?

Parallel Axis Theorem: 

The momentum of inertia depends upon the axis of rotation

To find the moment of inertia of an off center axis: I = Icom + Md2 

12.5 Torque: 

The ability of a force to a cause a rotation depends on three factors:

1) Magnitude of the Force, F

2) Distance, r, from the point of application to the pivot

3) Angle at which the force is applied

a) Angle is measured counterclockwise from the dashed line of the rotation of axis All these factors add up to create Torque​, T

T = rFsin(θ)

Gravitational Torque = Tgrav = -Mgxcom 

12.6 Rotational Dynamics: 

T = mr2α

Tnet =Iα

12.7 Rotation About a Fixed Axis: 

Just putting the equation Tnet =Iα into use

12.8 Static Equilibrium: 

Just how:

Fnet = 0 >> a = 0

Tnet = 0 >> α = 0

12.11 Angular Momentum: 

r = particles position

p = mv (momentum as we know from previous chapters)

Angular Momentum and Angular Velocity:

L = Iw, in the direction of the right hand rule

____________________________________________________________________________ Chapter 13 - Newton’s Theory of Gravity (really not much to this chapter): 13.3 Newton’s Law of Gravity: 

g = v2/r >> v = (gr)^(½)

Two masses create a gravitational force on each other: F1on2 = F2on1 = (Gm1m2)/r2 G = 6.67 x 10-11(Units are Nm2/kg2)

13.5 Gravitational Potential Energy:

13.6 Satellite Orbits and Energies (probably won't be asked any of this): F2on1 = (Gm1m2)/r2 = mar = mv2/r

M = more massive body

m = lesser, which is always the satellite

(satellite is just a term for a smaller object that orbits a larger object)