# 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.

### 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. ### TORQUE

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

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

Displacement

Velocity

Acceleration

### Rotational (Angular) Motion

Displacement

Velocity

$\omega =\frac{∆\theta }{∆t}$

Acceleration

$\alpha =\frac{∆\omega }{∆t}$

x = displacement

ʋ = velocity

a = acceleration

θ = angular displacement

ω = angular velocity

α = angular acceleration

t = time