Final-exam-review - Summary Physics for Life Science Majors PDF

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Physics 6A Final Exam Review Sheet

Peter Heuer, December 12th, 2014

This review sheet is not intended to be all-inclusive, but rather to be guide to the most important concepts and equations.

Math Review: Cross Products - A cross product is an operation that takes two vectors and returns a vector that is perpendicular to BOTH of the original vectors. ~ =B ~ × C. ~ If we only care about the magnitude of the vector (always in this class), this - The cross product is written A ~ ~ ~ ~ and C. ~ becomes |A| = | B||C|Sin(θ) Where θ is the angle betweeen B ~ and C ~ are paralell, Sin(θ) = 0, so |A| ~ = 0. When B ~ and C~ are perpendicular, Sin(θ) = 1, so | A| ~ = | B|| ~ C|. ~ - When B ~ or C ~ to the other vector therfore doesn’t contribute to the cross product, we - Since the paralell componet of either B ~ ~ ~ ~ ~ ~ can write |A| = | B⊥ ||C| or |A| = | B||C⊥ |

Circular Motion - If an object is moving in a circle, it must be experiencing a NET inward force. This net force is the centripetal force. - What are the analagous angular quantities for force, mass, acceleration, momentum, and velocity? What are the angular equivalents of Newton’s law and the kinematics equations? - In rotational motion, all the quantities are defined with respect to some point that we are rotating around! It does not make sense to, for example, add two angular velocities that are about two different points. - What is the rotational kinetic energy of a spinning object?

Torque - What is a torque, and how is it different than a force? - Why (and when) does finding a torque require taking the perpendicular component of a force or distance? How does this relate to the cross-product definition of torque?

Moment of Inertia - Just as mass measures how hard something is to move, moment of inertia measures how hard something is to spin. - The moment of inertia depends what point you are rotating around! - Moments of inertia about the same point and in the same direction can be added.

Angular Momentum - Angular momentum is the rotational analog to linear momentum - Can an object moving in a straight line have angular momentum? - Angular momentum is always conserved if there are no external torques!

Statics - The goal of statics is to find the forces in a system of objects that are not moving. - In this case, the sum of forces as well as the sum of torques (about ANY axis) on a system must be zero!

Physics 6A Final Exam Review Sheet

Peter Heuer, December 12th, 2014

Not all of these equations are true and/or useful in all situations.While studying, ask yourself when each of these equations apply!

Circular Motion

Moment of Inertia

Coorespondence with Linear Motion:

Moment of Inertia of a Point Particle

- v → ω, ω =

v r

- m → I, I =

X

I = mr2

Angular Momentum

mi r2i

i

Angular Momentum Conservation

a - a→α, α= r

~Li = ~Lf

- F → τ , τ = ~r × F~ = rF⊥

~L = ~r × p~

Newton’s Law

L = rp⊥

X

τ = Iα L = Iω

Centripetal Force Fc =

mv2 r

τ=

∆L ∆t

Statics

Torque ~τ = ~r × F~ τ = rF⊥

X

F~ = 0

X

~τ = 0...