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Calculating average speed
 d = distance
 t = time

Calculating average velocity
 displacement over time elapsed

Calculate average acceleration
 change in velocity over elapsed time

Relate change in velocity, acceleration, and time without position.
1dimensional, constant acceleration

Relate change in position, initial velocity, acceleration, and time without final velocity. 1dimensional, constant acceleration

Relate change in velocity, acceleration, and change in position without time. 1dimensional, constant acceleration

Free fall from 0 velocity
 g = 9.8m/s^2
 h = height of fall

For a vector of magnitude v making an angle θ with the xaxis, what are the components in 2dimensions?

Centripetal acceleration toward the center of a circle with radius r for an object traveling with constant speed v

Newton's first law of motion (Equilibrium)
Every body continues in its state of rest or of uniform speed as long as no net force and no net torque act on it.

Newton's second law of motion (Dynamics)
acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. Direction of a corresponds to direction of net F action on the object

Newton's third law of motion
Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.

Instantaneous velocity if position, x, as a function of time, t, is given as:

Relative motion in a moving frame, B.
 vA is object's velocity in a stationary frame
 VB is the velocity of the frame



Projectile Motion: Horizontal Range and flight time if start and end height are equal.


Projectile motion x and y travel components
t in x and y equations is the same, no acceleration in the x direction


Centripetal force in uniform circular motion


Relate centripetal acceleration, orbital period, and radius

Hooke's Law of an ideal spring over a limited range of stretch/compression relates Force with distance of stretch given a constant, k.

Motion on an inclined plane (ignoring friction)


Force of kinetic friction

Drag force moving through a fluid; relating density, area, and speed.
 C is the experimentally determined drag coefficient, ρ is the fluid density, A is the cross sectional area of the object, v is speed
 Direction opposite the object's motion relative to the fluid

Pulleys and opposing forces including friction (modified Atwood machine with opposing dangling masses A & C and mass B between them on a frictional surface)

Universal Gravitation  the force of gravity between any 2 objects
m's are masses; r is the centercenter distance

Universal Gravitation in a Circular Orbit

Torque (twisting force)
 F is force applied
 l is the length of the lever arm

Work (in Joules, J) done by a constant force of magnitude F on an object as it is displaced by a distance, d at an angle θ to each other.

Work from a varying force (1dimension or 3D)

Work from a spring (force varies with distance)

Fundamental Forces
 Gravitational  attractive force between all matter
 Electroweak (electromagnetic and weak nuclear)  virtually all of the nongravitational
 Color force (nuclear strong)  force between quarks, holds protons and neutrons together

Kinetic energy, K, for a mass, m, traveling at a speed, v.

Workenergy theorem: relating work due to nonconservative forces, W_nc and energy
The sum of the changes in kinetic, potential, and internal energy due to friction

Net Work and Kinetic energy

Conservative forces
 Gravitational, Elastic spring, & Electric forces
 Path Independent

Nonconservative Forces
 Friction
 Air Resistance
 Tension
 Normal Force
 Propulsion of a motor
 NOT path independent

Conservation of Mechanical Energy (ignores nonconservative forces)

Potential energy is the negative of the work done by a conservative force (general)

Potential energy with force and path parallel

Potential Energy with a constant force

Gravitational Potential Energy
 (close to Earth's surface)
 Generally:

Elastic (spring) potential energy
Set U=0 @ x=0:

Rest mass energy  the energy inherent to a particle by nature of it having a mass.

Power, P, is the rate at which work is done. Also described in terms of force, F, and velocity, v and the angle, θ, between them.
in Joules/sec = Watts

Conservation of linear momentum
 Total momentum remains unchanged

Impulse
impulse = change in momentum = product of average force over a time interval

Elastic collisions: bodies do not stick together, internal forces conservative, no sound or heat

Totally Inelastic Collisions: bodies stick together, maximum loss of mechanical energy that supports conservation of momentum

Elastic collisions, special cases relating m1 and m2 and final velocities

Center of Mass  average location for the total mass of the system

Density and Specific Gravity

Pressure (generally)
Force over Area in Pascals (Pa)

Hydrostatic Pressure at a fixed depth, y.

Buoyant Force, upward and equal to the weight of the fluid that the object displaces.
Density x volume = mass

The continuity equation describes volume flow rate as a function of the crosssectional area of the pipe and the velocity of the fluid.

Bernoulli's Equation  pressure energy, potential energy, and kinetic energy
Pressure + Potential (density*gh) + kinetic (velocity) energies in total don't change

Elastic Modulus of a solid (equation)

3 types of modulus of elasticity
 Young's modulus (E) for tensile stress (2 equivalent opposing parallel forces in same plane)
 Shear modulus (G) for shear stress (tensile but not lined up in same plane)
 Bulk modulus (B) for compression and expansion (forces from all sides)
 High modulus is rigid (metal and ceramic)
 Low modulus is elastic (rubber)



Sound Decibels
a difference of 10dB means intensity differs by a factor of 10 (90dB is 10 times louder than 80dB)

Standing waves  both ends fixed or free
 n=1, 2, 3, ...
 L= string or pipe length
 each end is a node or antinode

