Mechanics

NEWTON'S LAWS

1ST LAW

An object at rest stays at rest and an object in motion stays in motion with the same speed and direction unless acted upon by an outside force.

2ND LAW

A force is equivalent to an object's mass multiplied by its acceleration.

f o r c e = m a s s * a c c e l e r a t i o n

3RD LAW

For every action, there is an equal and opposite reaction.

MECHANICS

Describes the motion of objects. There are three branches of classical mechanics:

STATICS

the study of equilibrium and its relation to forces

KINETICS

the study of motion and its relation to forces

KINEMATICS

the study of motion without considering the forces that cause the motion

KINETICS

The relationship between motion and its causes, specifically forces and torques.

FORCE

An interaction between objects, such as a push or pull.

Figure: Free body diagram showing the forces involved when of a skateboarder grinds down a rail.

A diagram showing the kinetics of a skateboarder grinding down a rail.

TORQUE

A force that causes an object to rotate about an axis.

Figure: Torque is a twisting force that tends to cause rotation.

A diagram explaining torque.

KINEMATICS

DISTANCE

a scalar quantity that describes the total amount the object has moved.

DISPLACEMENT

a vector quantity that refers to the object's change in position.

SPEED

The rate of change of distance over time.

VELOCITY

Velocity quantifies the rate of change of displacement over time.

ACCELERATION

A vector quantity that defines the rate of change of velocity with respect to time.

KINEMATIC FORMULAS

Translational (Linear) Motion

Displacement

∆ x = x_{f} - x_{i}

Velocity

v = \frac{∆ x}{∆ t}

Acceleration

a = \frac{∆ v}{∆ t}

Rotational (Angular) Motion

Displacement

∆ θ = θ_{f} - θ

Velocity

ω = \frac{∆ θ}{∆ t}

Acceleration

α = \frac{∆ ω}{∆ t}

x = displacement

ʋ = velocity

a = acceleration

θ = angular displacement

ω = angular velocity

α = angular acceleration

t = time