Human Computer Interface Technology

Physics Review Lecture
September 25, 2002

*Copyright 1997-2002,
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: 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


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.


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