Interactive Arts Technologies
Physics Review Notes
February, 2000
Perry R. Cook,
Princeton University
Basic Newtonian Physics
Position and its derivatives
Position as function of time:
- Velocity as function of time is rate of change of Position with respect to time.
- Acceleration as function of time is rate of change of Velocity with respect to time.
Units: m (meters) and s (seconds)
- Position: m
Velocity: m/s
Acceleration: m/s/s = m/s^2
Force
- Force: F = ma (Newton's 2nd Law (with m = constant))
- Acceleration due to gravity, at sea level, on earth, is:
- Force due to gravity (sea level, earth) is: mg Newtons
- Frictional Forces:
- When stationary, the coefficient of static friction is:
- When moving, the coefficient of kinetic friction is:
- Force due to friction acts opposite other forces,
and is equal to
Example:
- When stationary, the coefficient of static friction is:
Energy (work) and Energy Flow
- Energy: W = F x (force through a distance, if F is constant)
- Power: = Energy flow, or the time rate of work = dW(t)/dt
- Potential Energy: Potential to do work because of position in a field
- In a conservative field, potential (and work)
only depends on
initial and final positions, not on path or time taken to traverse it.Example: Gravitational Potential Energy =
- Kinetic Energy: Ability to do work because of mass
in motion
Note that Kinetic Energy being related to the square of the velocity means that stopping a car takes four times the distance (constant frictional forces) if the car is going twice as fast.
- Energy is Conserved, A Very Important Physical Concept!!!
Example: Potential and Kinetic energy, dropping a ball
Initial Potential + Initial Kinetic = Final Potential + Final Kinetic
Mass cancels!! (Galileo and later some moon-walkers proved this experimentally)
- Mass is Conserved, Another Very Important Physical Concept!!!
Example: If I pound water into a hose, it either comes out the other
end or the hose eventually blows up. Mass is conserved.
Rotational Frames of Reference
- All of the above still works, just adjusted slightly
Example: A fulcrum with a pivot at 1/3 its length will balance with
twice as much mass on the short end as on the long end.Assume it's balanced and at rest (acceleration = 0)
- Rotational Energy:
The Basic 2nd Order Mechanical System
A spring with constant k (Force = -k y)
A mass with mass m
Some oil with damping R (Force = -R v)
y is the signed displacement from equilibrium (at rest with y = 0).
Minus sign on spring term means force acts to restore mass to rest position.
Minus sign on damping term means force acts against motion,
proportional to velocity.
Solutions:
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