# 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:  ## 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:  * Permission to make digital or hard copies of part or all
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