CH. 2 | Motion

What is Motion?

1) Change of position

2) The passage at time

2 Fundamental components of Motion

• Change in position

• Change in time

3 Important combinations of length and time

• Speed

• Velocity

• Acceleration

Speed

• Change in position with respect to time

• tells you how FAST something is moving

Average speed

• Most common measurement

Instantaneous speed

• Time interval approaches zero

• speed at any specific instant

Constant speed

• Moving over equal distances in equal periods of time

Velocity

• Describes speed (How fast it is going?) and direction (Where it is going?)

• Graphical representation of vectors: length = magnitude; arrowheads = direction

• tells you how fast and in what DIRECTION

Acceleration

• Rate at which motion changes over time

• Speed and Direction can change

• Can be negative

Uniform Acceleration

• Constant, straight-line acceleration

• Average velocity simply related to initial and final velocities in this case
  - decrease in velocity → negative acceleration → deceleration

Force

A push or pull capable of changing an object’s state of motion.

• Overall effect is determined by the (vector) sum of all forces - the “net force” on the object

• net force : the sum of all forces acting on an object

Fundamental Forces

• Gravitational

• Electromagnetic

• Weak force

• Strong force

Balanced and Unbalanced Forces

• Motion continues unchanged without unbalanced forces

• Retarding force decreases speed

• Boost increases speed

• Sideways force changes direction

Free Falling Objects

Free fall

• Falling under influence of gravity without air resistance

• Distance proportional to time squared

• Speed increases linearly with time

• Trajectories exhibit up/down symmetries

• Acceleration same for all objects

Compound Motion (3 Types)

• Vertical motion

• Horizontal motion

• Projectile motion

Projectile Motion

An object thrown into air

• i.e., football

• Vertical projectile

• Horizontal projectile

3 Laws of Motion

Isaac Newton

• Developed calculus and a law of gravitation

• Essential idea - forces

Newton’s First Law of Motion

“The Law of Inertia”

• Every object remains at rest or in its state of uniform straight-line motion unless acted upon by an unbalanced force

  → net force > (greater than) 0

• An object in motion stays in motion

• An object in rest stays at rest

• Inertia resists any changes in motion

Newton’s Second Law of Motion

F = ma

1 newton = 1 N = 1 kg*m ∕ s²

• Forces cause accelerations

• Unit = Newton (N)

• Proportionality constant = mass

• More force, more acceleration

• More mass, less acceleration

Weight and Mass

Weight

• Force of gravity acting on the mass

Mass

• Quantitative measure of inertia; the amount of matter

Kilogram

• Measure of mass

Picture

Newton’s Third Law of Motion

F _{A due to B} = F _{B due to A} 

• i.e., 30N = 30N

• Relates forces between objects

• Source of force - other objects

• Whenever 2 objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object

• A single force does not exist by itself

Momentum

monmentum = mass * velocity

p = mv

Important property closely related to Newton’s Second Law

• Includes effects of both motion (velocity) and inertia (mass)

Conservation of Momentum

The total momentum of a group of interacting objects remains the same in the absence of external forces

Applications: Collisions, analyzing action/reaction interactions

Impulse

impulse = Ft

• A force acting on an object for some time (t)

• An impulse produces a change in momentum

Applications: airbags, padding for elbows and knees, and projectile plastic barrels on highways

Forces and Circular Motion

Circular motion = accelerated motion (direction changing)

• Centripetal (center seeking) acceleration is present

• Centripetal force must be acting

• Centrifugal force - apparent outward tug as direction changes

• Centripetal force ends: motion = straight line

Newton’s Law of Gravitation

F = G m₁m₂ ∕ d²

• Gravity is an attractive force between all masses

• Proportional to product of the masses

• Inversely proportional to separation distance squared

• Provides centripetal force for orbital motion