# 2D Kinematics

## Two Dimensional Kinematics

• Velocity = speed in a given direction e.g 3 m/s east or 3 mph north (or -3m/s if the motion is one dimensional and the positive and negative directions have already been specified).

Motion can be described well with graphs or with equations. The three most useful types of motion graphs are the displacement-time graph, the velocity-time graph and the acceleration-time graph. Each graph type is interpreted differently:

Displacement-time graphs

• slope of graph = velocity
• Steeper slope = higher velocity
• Zero slope = stationary
• Negative slope = moving backwards

Velocity-time graphs

• slope of graph = acceleration
• Steeper slope = higher acceleration
• Zero slope = constant velocity
• Negative slope = deceleration (negative acceleration) = slowing down (or speeding up while traveling backwards)
• Area under graph = displacement

Acceleration-time graphs

• Area under graph = change in velocity

## Scalars and Vector

### 4.1 Projectile Motion

'Projectile motion' is the motion of an object moving near the earth and acted on by gravity alone (no air resistance). The key to understanding projectile motion is to consider the horizontal and vertical components of the motion separately, for they are independent of one another

For objects in projectile motion:

• the horizontal component of its velocity does not change (no horizontal force, so no horizontal acceleration).
• The vertical component is subject to a constant acceleration due to the constant vertical force.

### 4.2 Circular Motion

• An object rotates when it turns around an internal axis; it revolves when it turns around an external axis.
• Rotational speed is the number of rotations or revolutions made per unit of time.
• The SI unit for rotational speed is the hertz (Hz). 1 Hz = 1 rotation per second.
• An object moving in a circle is acted on by a net force towards the center, called the centripetal force.
• The magnitude of the centripetal force is given by Fcent = mv² / r
• When an object moves in a circle, there is NO force pushing the object outward from the circle.From within a rotating frame of reference, there may seem to be an outwardly directed ('centrifugal') force, but this is in fact an illusion, a 'pseudo-force'. In reality, the net force is always inwards.