Motion

Motion occurs when an object moves from one point to another. The study of motion without considering the force that causes it is called Kinematics. Every motion is caused by a Force.

Types of Motion

  1. Translational or Linear Motion: Movement of a body from one point to another without rotation.
    1. A car traveling between two stations.
    2. A student moving from one class to another.
    3. An airplane flying from Lagos to Ibadan.
  2. Rotational Motion: Movement of a body in a circular path.
    1. Rotation of a fan blade.
    2. Rotation of a car wheel.
    3. Earth's rotation around the Sun.
  3. Random Motion: Irregular movement with no specific direction.
    1. Movement of gas molecules.
    2. Movement of a housefly.
    3. Movement of a woman in the market.
  4. Oscillatory or Periodic Motion: A to-and-fro movement that regularly returns to its original position.
    1. Motion of a loaded test tube.
    2. Motion of a suspended pendulum bob.
    3. Motion of a spiral spring.

Speed

Speed is defined as the rate of change of distance with time. It is given by:

\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\Delta s}{\Delta t} \]

In terms of initial and final values:

\[ \text{Average Speed} = \frac{s_{\text{final}} - s_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}} \]

The SI unit of speed is meters per second (m/s).

Velocity

Velocity is defined as the rate of change of displacement with time. Unlike speed, velocity considers direction.

\[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{\Delta x}{\Delta t} \] \[ \text{Velocity} = \frac{x_{\text{final}} - x_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}} \]

Rectilinear Acceleration

Rectilinear acceleration refers to the rate of change of velocity along a straight-line path. When the velocity of an object changes, it is said to accelerate or decelerate.

Acceleration is defined as the rate of increase of velocity with time, while deceleration (also called retardation or negative acceleration) is the rate of decrease of velocity with time.

\[ \text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}} \] \[ a = \frac{v_{\text{final}} - v_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}} \]

Equations of Uniformly Accelerated Motion

\[ s = \frac{(v + u) t}{2} \quad \text{(Equation 1)} \] \[ v = u + at \quad \text{(Equation 2)} \] \[ v^2 = u^2 + 2as \quad \text{(Equation 3)} \] \[ s = ut + \frac{1}{2} at^2 \quad \text{(Equation 4)} \]

Where:

Motion Under Gravity: Gravitational Acceleration

When an object is thrown upwards or released from a height, its motion is affected by gravity.

The equations of motion for gravitational acceleration are derived from the equations of motion for rectilinear acceleration:

Equations for a Body Thrown Upwards

Equations for a Body Falling Downwards

Graphs of Motion

The motion of an object is best represented using graphs. The three main types of motion graphs are:

  1. Distance-Time Graph
  2. Displacement-Time Graph
  3. Velocity-Time Graph

Distance-Time Graph

In a distance-time graph, the slope or gradient of the graph represents the speed of the object.

Distance time Diagram Credit: Geeksforgeeks

Displacement-Time Graph

A displacement-time graph can be either linear or curved. For a linear graph, the gradient represents the velocity of the object.

Displacement-time graph Credit: Siti Amira Othman on Researchgate

Velocity-Time Graph

The velocity-time graph provides more useful information than the other two graphs, as it can be used to determine:

velocity-time graph Credit: Teachoo

In some cases, the motion of objects on a velocity-time graph forms geometric shapes such as squares, triangles, trapeziums, or rectangles. The total distance covered by the object is equal to the sum of the areas of these shapes.

Relative Motion

When two objects, A and B, are moving along a straight line, the velocity of A relative to B is determined by adding the velocity of B, reversed, to the velocity of A.

For example, if a car is traveling at 100 km/h on a straight road and overtakes a bus moving in the same direction at 60 km/h, the velocity of the car relative to the bus is calculated as:

(-60 + 100) = 40 km/h

If the car and bus move in opposite directions with velocities of 100 km/h and 60 km/h respectively, the velocity of the car relative to the bus is:

(-(-60) + 100) = (60 + 100) = 160 km/h

Note: When the velocities are not along the same straight line, the parallelogram law should be used, since velocity is a vector quantity that takes both magnitude and direction into account.

Force and Friction

Force is any influence that changes or tends to change the state of rest or uniform motion of a body.

Types of Force

  1. Contact Force: Forces that act through direct contact, such as frictional force, tension, and reaction force.
  2. Force Field: Forces that act at a distance, such as gravitational, electric, and magnetic force fields.

Simple Idea of Circular Motion

When an object moves at a constant speed along a circular path, it is said to be in uniform circular motion. Examples include:

  1. The moon orbiting the Earth.
  2. The planets revolving around the Sun.
  3. A stone tied to a string and whirled in a circular motion.

Characteristics of Circular Motion:

  1. Constant speed
  2. Changing velocity
  3. Centripetal acceleration

Centripetal Acceleration: The acceleration directed towards the center of the circular path, given by:

$$ a = \frac{V^2}{r}$$

where v is the uniform speed and r is the radius.

Centripetal Force: The inward force required to maintain circular motion, given by:

$$ F_T = \frac{mv^2}{r}$$

where m is the object's mass.

Centrifugal Force: The reaction force that pushes a body away from the center, acting opposite to centripetal force.

Centrifuge: A device that separates suspended particles from a liquid using centrifugal force.