AP Core Concepts & Equations Flashcards
Kinematics Equation Not Given:
Delta X=
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
If an object launches horizontally then the inital velocity in the y dimension=
0
At the higest point a projectile has ___ vertical velocity by the acceleration = ____
NO, 9.8
Define: inertia
The tendency of an object to resist any attempt to change its velocity.
Define: Force
Strength or energy as an attribute of physical action or movement.
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.
Applications of Kinematics
Projectile Motion
Using one known equation (such as position) to determine the rest
Interpreting Graphs
ΣF=
ma
Newtons Second Law
ΣF=ma
Friction=
µn
Centripetal Acceleration=
v2/r
Force of a Spring=
-kx
Hookes Law
Fspring= -kx
Only ____ springs obey Hookes Law
Linear
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.)
x=
y=
Ø=
x=rcosØ
y=rsinØ
Øtan-1(y/x)
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)
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.
Simultaneous equations are often easier to solve using _____ than they are using _____.
elimination (adding, subtracting, or dividing), substitution
______ friction is stronger than ______ friction.
Static, Kinetic
Resistive forces come in the form:
F= -bv where b=drag coefficient, v=velocity
Because resistance increases with speed the object will eventually reach a ___________.
terminal velocity.
Terminal Velocity:
a=
ΣF=
bv=
Vt=
(if gravity is involved)
a=0
ΣF=0
bv=mg
VT=mg/b
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)=
mv
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=ICM + MD2
T (torque) =
requirements for this to be true
other expressions
r x F
Naturally perpendicular
r x FsinØ, ad-bc
ac =
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=
wo + αt
Ø=
*rotational motion
Øo + wot + 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=Icm + 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.
- Where the force is active
- Identify your pivot point.
REMEMBER FORCES ARE ______________.
NOT TORQUE
