Kinematics in one dimension
Constant acceleration equations for motion in one dimension
VECTORS
1: (magnitude) and θ (direction)
2: (usually there is no z component)
Adding two vectors mathematically:
Constant acceleration equations now! (we can look at x and y motion separately)
Uniform Circular Motion (pointing toward center of circle)
Newton's Second Law
Component form:
Friction
Static Friction
Kinetic Friction (note: not vector equations)
Gravitation
the direction is from the mass experiencing the force toward the other mass G=6.67 x 10-11 N m2 kg-2
Work
(for constant force)
Kinetic Energy
A cool equation:
Hooke's Law (spring force):
Work done by a spring:
Gravitational Potential Energy near the surface of the Earth:
you can choose where h=0
Gravitational Potential Energy not near surface of the Earth:
Elastic Potential Energy due to the spring force:
Mechanical Energy:
Energy Conservation:
Power
Momentum
Newton's 3rd Law, momentum-style:
Momentum of a system:
If a collision is elastic, then
Center of Mass:
and similarly for y and z.
where l is the arclength, θ is the angle (in radians), and r is the radius.
l and r have to be in the same units.
360° = 2π radians = 1 revolution
Angular displacement
Angular velocity (speed)
Angular acceleration
Constant alpha equations
Equations relating linear (tangential) stuff to rotational stuff
vtan = rω
atan = rα
Moment of Inertia
Rotational Kinetic Energy
Vector (Cross) Product
Direction is given by the Right Hand Rule
Torque!
Newton's Second Law in the rotational world
Angular Momentum of a particle:
Angular Momentum of a system of particles:
Angular Momentum of a rotating body:
Equilibrium: and
Static means that and
Simple Harmonic Motion
(kSHM is just whatever positive constant happens to be there.)
Our solution is:
Relations between ω, kSHM, the period T, and frequency f are:
and various combinations thereof.
From x(t) we can find v(t) and a(t):
and
So and
Energy!
Rotational Simple Harmonic
(kSHM is just whatever positive constant happens to be there.)
Our solution is:
θmax is the Amplitude, ω is the angular frequency, and φ is the phase factor (which takes care of initial conditions.
Wave equation:
D(x,t) = A cos ( kx – wt + φ )
k = wave number = 2π/λ
w = angular frequency = 2πf
A = amplitude
Φ = phase constant
v = f * λ
Thermodynamics
Thermal Expansion:for linear expansion
for volume expansion
OR
Ideal Gas Law:R = 8.315 J/(mol*K)for Chemists
Internal Energy of a gas
Specific Heat
where c is the specific heat
Latent Heat
where L is the latent heat
Quadratic Formula:
for , the value of x is given by: