AP Core Concepts & Equations Flashcards by Katie Worms

Kinematics Equation Not Given:
Delta X=

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If projectile trajectory is symmetric:

angle up=angle down

speed up=speed down

time up=time down

projectile position graph=parabola curving down

projectile velocity graph=diagonal line with slope=9.8

projectile acceleration graph=flat line=9.8

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If an object launches horizontally then the inital velocity in the y dimension=

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At the higest point a projectile has ___ vertical velocity by the acceleration = ____

NO, 9.8

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Define: inertia

The tendency of an object to resist any attempt to change its velocity.

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Define: Force

Strength or energy as an attribute of physical action or movement.

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Define: Tension

the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three dimensional object.

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Applications of Kinematics

Projectile Motion

Using one known equation (such as position) to determine the rest
Interpreting Graphs

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ΣF=

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Newtons Second Law

ΣF=ma

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Friction=

µn

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Centripetal Acceleration=

v²/r

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Force of a Spring=

-kx

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Hookes Law

F_spring= -kx

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Only ____ springs obey Hookes Law

Linear

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Applications of Newton’s Laws

(8: F,F,P,R,S,T,T,R)

Free body diagrams that are balanced
Free body diagrams that are accelerating
Pulleys
Ramps
Satellites (Centripetal Acceleration)
Turning Corners
Tension in a rope attached to a circling object
Resistive Forces (Air resistance, drag, etc.)

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Ø=

x=rcosØ
y=rsinØ

Øtan^-1(y/x)

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Newton’s Three Laws

Law 1: Balanced Forces (Object in motion stays in motion…)
Law 2: Unbalanced Forces (F=ma)

Law 3: Pair Forces (action, reaction)

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If you change your axis to match a ramp and the angle of the ramp is measured from the horizontal, then. . .

. . . sin and cos switch dimensions.

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Simultaneous equations are often easier to solve using _____ than they are using _____.

elimination (adding, subtracting, or dividing), substitution

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______ friction is stronger than ______ friction.

Static, Kinetic

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Resistive forces come in the form:

F= -bv where b=drag coefficient, v=velocity

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Because resistance increases with speed the object will eventually reach a ___________.

terminal velocity.

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Terminal Velocity:
a=

ΣF=

bv=

V_t=

(if gravity is involved)

a=0

ΣF=0

bv=mg

V_T=mg/b

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To solve a resistive system:

ΣF=mg-bv ma=mg-bv a=(mg-bv)/m dv/dt=(mg-bv)/m dv/dt=g-bv/m

STOP: GO OVER LONG 16 STEPS

Solution of Resitive System with Gravity

V=mg/b(1-e^-bt/m)

Object in Free Fall w/ Air Resistance Position Graph \*assuming down is positive

Curves at first, then approaches a straight diagonal line with slope=Terminal Velocity

Object in Free Fall w/ Air Resistance Velocity Graph \*assuming down is positive

Slope=9.8 but then curves towards a horizontal asymptote (terminal velocity)

Object in Free Fall w/ Air Resistance Acceleration Graph \*assuming down is positive

Starts at 9.8 and curves towards a horizontal asymptote (a=0)

Object in Free Fall w/ Air Resistance Projectile \*assuming down is positive

Time up \< Time down because on the way down air resistance acts like a parachute Won't go as high, crests before down time.

p (momentum)=

J= \* if force is constant

FΔt

J= \*if force fluctuates

∫Fdt=ΔP

F= \*relating to momentum

dp/dt

Center of Mass=

Σmr/Σm

Applications of Momentum

Collisions Calculating Velocity before and after an action such as throwing, catching, pushing, jumping, exploding, etc.

Momentum is always \_\_\_\_\_\_.

conserved.

Momentum links to _______ like work links to \_\_\_\_\_\_\_.

forces, energy \*think derivatives

Force= _____ derivative of \_\_\_\_\_.

time derivative of momentum

Impulse=

change in momentum area under a force vs. time graph

Changes in momentum come from two sources: ______ & \_\_\_\_\_\_.

force & time

When calculating the center of mass, always place one of your objects \_\_\_\_\_\_\_\_\_\_.

on the origin.

Use the center of mass for questions involving \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

gravitational potential energy.

If two objects collide and stick together then kinetic energy will _____ conserved and ____ heat will be lost from the system.

not be, a lot of

If a collision is _______ elastic the kinetic energy will be conserved.

Angular Velocity (Units)

rad/s

Define: Torque

a measure of the turning force on an object.

Define: Moment of Inertia

a quantity expressing a body's tendency to resist angular acceleration. It is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

Define: Angular Momentum

The Cross Product of the particle's instantaneous position vector r and its instantaneous momentum p: L=r x p

Define: Parallel Axis Theorem

The moment of inertia about any axis parallel to and a distance D away from the axis is I=I_CM+ MD²

T (torque) = requirements for this to be true other expressions

r x F Naturally perpendicular r x FsinØ, ad-bc

a_c=

w²• r

I = \*uniform density

∫r²dm

I = Σ

Σmr²

v= \*involving rotational motion requirements for this to be true

rw only if NOT slipping

L (angular momentum)=

r x p= Iw

K= \*for rotational motion

½Iw²

w_o + αt

Ø= \*rotational motion

Øo + w_ot + ½αt²

ΣT(torque)=

Iα

Applications of Rotational Motion | (7: p,w,s,o,b,p,r)

Pulleys with inertia Wrenches & other tools Spinning Objects Objects in Orbit (Conservation of Angular Momentum) A bar that Pivots as it falls Pendulums/Swings Rolling

Cross products are all about being \_\_\_\_\_\_\_\_\_.

Perpendicular

JUST READ THIS r x F=rFsinØ (or) r x F = perpendicular distance times F The angle in the above equation is the angle between the position vector and the force vector. It has nothing to do with the x-axis.

Every linear entity has an ______ counterpart.

angular

Linear = assuming,

Angular \* Radius assuming no slipping

Moment of Interia Hoop or thin cylindrical shell

MR²

Moment of Interia Hollow Cylinder

½M(R₁² + R₂²)

Moment of Interia Solid Cylinder or Disk

½MR²

Moment of Interia Rectangular Plate

(1/12)M(a² + b²)

Moment of Interia Long thing rod with rotational axis through center

(1/12)ML²

Moment of Interia Long thin rod with rotation axis through end

(1/3)ML²

Moment of Interia Solid Sphere

(2/5)MR²

Moment of Interia Thin Spherical Shell

(2/3)MR²

Parallel Axis Theorem: I=

I=I_cm+ MD²

Torque is the _____ derivative of \_\_\_\_\_\_\_\_.

time, angular momentum

Angular motion has _____ & _____ just like linear motion.

momentum and energy

Rolling objects have both ______ and ______ quantities, but need enough _____ to prevent slipping.

linear and angular, friction

Spinning objects (the pivot is secured in place) have only ______ quantities.

angular

JUST READ THIS Free body diagrams work for angular motion as well. Just define which way of spinning is positive and negative.

Go over Right hand rule for the direction of angular momentum. Remember any object spinning has \_\_\_\_\_\_\_\_\_\_\_\_\_.

axis of rotation

An object does not need to be spinning or turning in order to have \_\_\_\_\_\_\_\_\_\_\_.

angular momentum.

An angular force diagram must show 1. 2.

1. Where the force is active 2. Identify your pivot point.

REMEMBER FORCES ARE \_\_\_\_\_\_\_\_\_\_\_\_\_\_.

NOT TORQUE

AP Core Concepts & Equations Flashcards

(84 cards)