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Laws of Motion
Law I
Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (Inertia)
Law II:
The acceleration of a body is proportional to the resulting force acting on the body, and this acceleration is in the same direction as the force.
Law III:
For every action there is an equal and opposite reaction.
Linear Motion
For Linear Physical Motion
Mass
Measure of the amount of matter in a body From Law II: Measure of the a body’s resistance to motion
Velocity
Change of motion with respect to time
Acceleration
Change of velocity with respect to time
Force
In short, force is what makes objects accelerate
Momentum
mass x velocity Another way of stating Law I: Momentum is conserved
Rotational Motion
For Rotational Physical Motion
Inertia
Measure of the amount/distribution of matter in a body From Law II: Measure of the a body’s resistance to motion
Angular Velocity
Change of rotation with respect to time
Angular Acceleration
Change of velocity with respect to time
Torque
In short, torque is what makes objects rotate
Angular Momentum
Inertia x velocity Another way of stating Law I: Momentum is conserved
Where we are
Object properties Position, orientation Linear and angular velocity Linear and angular momentum mass Calculate forces Calculate accelerations Using mass, momenta Update object properties
Where we are
State of object at any given time
position
rotation (in world coords) momentum angular momentum
) ( ) ( ) ( ) ( ) ( t L t M t R t s t S
Where we are
Derivative of object state
) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t t F t R t t v t L t M t R t s t S
& & & &
