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Calculating average speed
 - d = distance
- t = time
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Calculating average velocity
- displacement over time elapsed
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Calculate average acceleration
- change in velocity over elapsed time
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Relate change in velocity, acceleration, and time without position.
1-dimensional, constant acceleration
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Relate change in position, initial velocity, acceleration, and time without final velocity. 1-dimensional, constant acceleration
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Relate change in velocity, acceleration, and change in position without time. 1-dimensional, constant acceleration
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Free fall from 0 velocity
- g = -9.8m/s^2
- h = height of fall
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For a vector of magnitude v making an angle θ with the x-axis, what are the components in 2-dimensions?
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Centripetal acceleration toward the center of a circle with radius r for an object traveling with constant speed v
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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.
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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
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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.
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Instantaneous velocity if position, x, as a function of time, t, is given as:
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Relative motion in a moving frame, B.
- vA is object's velocity in a stationary frame
- VB is the velocity of the frame
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Projectile Motion: Horizontal Range and flight time if start and end height are equal.
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Projectile motion x and y travel components
t in x and y equations is the same, no acceleration in the x direction
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Centripetal force in uniform circular motion
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Relate centripetal acceleration, orbital period, and radius
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Hooke's Law of an ideal spring over a limited range of stretch/compression relates Force with distance of stretch given a constant, k.
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Motion on an inclined plane (ignoring friction)
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Force of kinetic friction
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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
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Pulleys and opposing forces including friction (modified Atwood machine with opposing dangling masses A & C and mass B between them on a frictional surface)
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Universal Gravitation - the force of gravity between any 2 objects
m's are masses; r is the center-center distance
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Universal Gravitation in a Circular Orbit
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Torque (twisting force)
- F is force applied
- l is the length of the lever arm
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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.
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Work from a varying force (1-dimension or 3-D)
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Work from a spring (force varies with distance)
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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
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Kinetic energy, K, for a mass, m, traveling at a speed, v.
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Work-energy 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
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Net Work and Kinetic energy
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Conservative forces
- Gravitational, Elastic spring, & Electric forces
- Path Independent
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Non-conservative Forces
- Friction
- Air Resistance
- Tension
- Normal Force
- Propulsion of a motor
- NOT path independent
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Conservation of Mechanical Energy (ignores non-conservative forces)
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Potential energy is the negative of the work done by a conservative force (general)
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Potential energy with force and path parallel
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Potential Energy with a constant force
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Gravitational Potential Energy
- (close to Earth's surface)
- Generally:
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Elastic (spring) potential energy
Set U=0 @ x=0:
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Rest mass energy - the energy inherent to a particle by nature of it having a mass.
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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
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Conservation of linear momentum
- Total momentum remains unchanged
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Impulse
impulse = change in momentum = product of average force over a time interval
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Elastic collisions: bodies do not stick together, internal forces conservative, no sound or heat
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Totally Inelastic Collisions: bodies stick together, maximum loss of mechanical energy that supports conservation of momentum
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Elastic collisions, special cases relating m1 and m2 and final velocities
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Center of Mass - average location for the total mass of the system
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Density and Specific Gravity
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Pressure (generally)
Force over Area in Pascals (Pa)
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Hydrostatic Pressure at a fixed depth, y.
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Buoyant Force, upward and equal to the weight of the fluid that the object displaces.
Density x volume = mass
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The continuity equation describes volume flow rate as a function of the cross-sectional area of the pipe and the velocity of the fluid.
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Bernoulli's Equation - pressure energy, potential energy, and kinetic energy
Pressure + Potential (density*gh) + kinetic (velocity) energies in total don't change
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Elastic Modulus of a solid (equation)
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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)
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Sound Decibels
a difference of 10dB means intensity differs by a factor of 10 (90dB is 10 times louder than 80dB)
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Standing waves - both ends fixed or free
- n=1, 2, 3, ...
- L= string or pipe length
- each end is a node or antinode
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