Inertia

 

- The tendency of an object to stay in its current state of

   motion or rest.

 

- Property of matter.

 

- Depends on mass only.

 

- Directly proportional to mass.

- As mass increases, inertia increases.

- As mass decreases, inertia decreases.

 

- Mass is sometimes defined as a measure of the amount

  of inertia in an object.

 

- Does NOT depend on speed. (non-relativistic)

 

- Is NOT a force.

Newton’s First Law of Motion

AKA: The Law of Inertia

 

1) An object at rest stays at rest, or

an object in motion at a constant speed in a straight line

stays in motion at a constant speed in a straight line,

unless/until some (non-zero, net) force acts on the object.

 

OR

 

2) If the net force acting on an object is zero, the object’s velocity is constant.

 

“Velocity is constant” means either, velocity = zero, OR

speed is constant and motion is in a straight line.

 

“Velocity is constant” means acceleration = zero.

 

3) If net force = zero, acceleration = zero.

 

Force is NOT required for an object to maintain motion (or a state of rest.)

 

Force is required for ANY change in an object’s motion (or state of rest.)

Force and Net Force

 

- A push or pull.

 

- A vector quantity.

- Magnitude and direction.

- Must be added vectorally.

 

- Measured in pounds, ounces, tons, newtons…

 

NET Force

The (vector) sum of all forces acting on an object.

 

No net force or net force = zero means either,

      1) no forces are acting at all,   OR

      2) the (vector) sum = zero.

 

An object moving at constant velocity feels no net force.

 

If a force is clearly being applied to an object that stays at rest, then the net force must still be zero.

 

Friction, tension, thrust, weight, drag, resistance are all forces.

Force Myths

 

Force of hand (or bat or racket or foot or…) stays with a thrown (or batted or hit or kicked or…) object (while it’s in flight.)

 

Force is required to keep an object moving.

 

The force required to push an object along at a constant speed is greater than the retarding forces (i.e., friction.)

 

Inertia is a force.

 

A force is a property of an object.

 

Air doesn’t exert a force.

 

Forces can exist in isolation.

 

Greater speeds require greater forces for equal accelerations.

 
Newton’s Second Law of Motion

AKA: The Law of Acceleration

 

If the net force on an object (of mass m) is not zero, then the object will accelerate in the direction of that net force with a magnitude that is proportional to the net force and inversely proportional to the mass of the object. Mathematically stated:

 

                        a = F / m

 

Most commonly remembered as:

 

                        F = m * a

 

If mass is measured in kg, acceleration in m/s2, then force will have units of  kg m/s2 or newtons (N).  (SI units)

 

If mass is measured in g, acceleration in cm/s2, then force will have units of  g cm/s2 or dynes. (cgs units)

 

If mass is measured in slugs, acceleration in ft/s2, then force will have units of  slugs ft/s2 or pounds (lbs).

Newton’s Third Law of Motion

AKA: The Law of Interaction

 

For every action…

 

If one object exerts a force on a second object, then the second object exerts an equal but oppositely directed force on the first object.

 

The reaction force (of #2 object on #1 object) is NOT a FBD force on object #2.

 

Action/reaction forces are DIFFERENT forces on DIFFERENT objects. They NEVER cancel out.

 

Forces cannot exist in isolation. (A “force” field is not a force…)

Mass versus Weight

 

Mass

- A measure of the amount of an object’s inertia.

- A measure of the amount of stuff in an object.

- A measure of an object’s resistance to acceleration.

- NOT a measure of the amount of space an object

   takes up.

- A scalar quantity.

- Independent of location/position.

- Depends on speed. (relativity)

- Proportional to the weight of an object.

- Measured in slugs (English) or kilograms (SI).

- Measured with a balance.

 

Weight

      - A measure of the force of gravity on an object.

      - A force.

      - A vector quantity.

      - Depends on location/position.

      - Depends on g. (Proportional to g.)

      - Proportional to the mass of an object.

      - Measured in pounds (English), newtons (SI),

         dynes, ounces, tons, etc…

      - Measured with a spring scale.

Mass versus Weight (continued)

 

Common usage: These two words are frequently interchanged, usually with no resulting confusion. (See the label on just about any canned or packaged food item.)

 

Science usage: There is a critical, non-trivial distinction between these two words and concepts. Failure to grasp that distinction will be detrimental to your success in related problems.


Newton’s Law of

Universal Gravitation

 

- Gravity is a consequence of mass.

- The force of gravity between two objects is directly

   proportional to the product of the objects’ masses.

- The force of gravity between two objects is inversely

   proportional to the square of the distance between

   the two objects’ centers of mass.

 

F = G m1 m2 / r2

 

G = Universal Gravitational Constant

    = 6.67 x 10-11 N m2 / kg2

 

Weight

 

            W = G ME m / rE2

 

            ME = mass of Earth (or whatever planet/moon/sun)

 

But, G, ME, and rE are all constants, therefore, G ME / rE2 is

also a constant.


Weight (continued)

 

G ME / rE2  =  9.80 m/s/s  =  g !!

 

W = m g

 

The force of gravity on an object, or, the weight of an object is equal to the mass of that object multiplied by the acceleration due to gravity (for whatever planet the object is on.)