Types of Motion

In Physics, motion is the change in the position of an object with respect to time and a reference point.
Different types of motion exist depending on the path followed by the object.

👉 The three fundamental types we study are:

1. Rectilinear or Translatory Motion
2. Circular or Rotatory Motion
3. Oscillatory or Vibratory Motion

2. 1. Rectilinear or Translatory Motion

Definition

An object is said to be in rectilinear motion (also called translatory motion) if it moves along a straight line.

Examples

• A car moving on a straight highway
• An apple falling from a tree.
• A ball rolling in a straight tunnel.

Key Points

• The direction of motion is fixed.
• The position of the object changes only along one dimension.
• This type of motion is the simplest to analyze using displacement, velocity, and acceleration.

Important Quantities

1. Displacement: [ s = x_2 – x_1 ]
2. Velocity: [ v = \dfrac{ds}{dt} ]
3. Acceleration: [ a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2} ]

🔗 Math Link:
All these relations use Differentiation.
👉 Click here to review Differentiation

3. 2. Circular or Rotatory Motion

Definition

An object is said to be in circular motion if it moves along a circular path while remaining at a constant distance from a fixed point (center).

👉 If the object rotates about a fixed axis, the motion is called rotatory motion.

Examples

• A satellite orbiting Earth.
• A fan blade rotating about its axis.
• A stone tied to a string and whirled in a circle.

Key Points

• The path of motion is a circle or an arc of a circle.
• The distance from the center remains constant (radius).

Important Quantities

1. Angular Displacement: [ \theta = \dfrac{s}{r} ]
   where [ s ] is arc length and [ r ] is radius.
2. Angular Velocity: [ \omega = \dfrac{d\theta}{dt} ]
3. Angular Acceleration: [ \alpha = \dfrac{d\omega}{dt} ]
4. Centripetal Acceleration: [ a_c = \dfrac{v^2}{r} = r\omega^2 ]
5. Centripetal Force: [ F_c = m a_c = \dfrac{m v^2}{r} ]

🔗 Math Link:
The relations use Differentiation.
👉 Click here to review What is Differentiation

4. 3. Oscillatory or Vibratory Motion

Definition

An object is said to be in oscillatory motion if it moves to and fro about a fixed mean position in a repeated manner.

👉 The restoring force always acts towards the mean position.

Examples

• A pendulum swinging to and fro.
• A mass attached to a spring.
• Vibrations of a guitar string.

Key Points

• The object moves repeatedly between two extreme positions.
• The time to complete one full oscillation is called the Time Period (T).
• Oscillations are often periodic (repeating at regular intervals).

Important Quantities

1. Displacement in SHM:
   [ x(t) = A \sin(\omega t + \phi) ]
   where:
   • [ A ] = amplitude (maximum displacement)
   • [ \omega ] = angular frequency
   • [ \phi ] = phase constant
2. Time Period:
   [ T = \dfrac{2\pi}{\omega} ]
3. Frequency:
   [ f = \dfrac{1}{T} ]

🔗 Math Link:
Oscillatory motion equations use Trigonometric Functions and Differentiation.

5. SI Units and Dimensional Formulas

6. Examples

1. Rectilinear Motion:
   A train moving straight from station A to B at constant speed.
2. Circular Motion:
   A stone tied to a string and whirled in a horizontal circle of radius 0.5 m.
3. Oscillatory Motion:
   A 2 kg mass attached to a spring oscillating on a frictionless surface.

7. Practice Questions (With Solutions)

Conceptual Questions

1. Give one example of rectilinear motion from daily life.
   • Solution: A car moving on a straight bridge.
2. Which type of motion is exhibited by the blades of a ceiling fan?
   • Solution: Circular or rotatory motion.
3. Define the time period of oscillation.
   • Solution: Time taken to complete one full cycle of oscillation.

Numerical Questions

4. A car moves with constant velocity of [ 20 , \text{m/s} ] for 10 seconds. Find its displacement.
   • Solution:
     [
     s = v t = 20 \times 10 = 200 , \text{m}
     ]
5. A stone is tied to a string of length [ 0.5 , \text{m} ] and rotated at speed [ 4 , \text{m/s} ]. Find centripetal acceleration.
   • Solution:
     [
     a_c = \dfrac{v^2}{r} = \dfrac{4^2}{0.5} = \dfrac{16}{0.5} = 32 , \text{m/s}^2
     ]
6. A simple pendulum completes 20 oscillations in 50 seconds. Find its time period and frequency.
   • Solution:
     [
     T = \dfrac{\text{total time}}{\text{number of oscillations}} = \dfrac{50}{20} = 2.5 , \text{s}
     ]
     [
     f = \dfrac{1}{T} = \dfrac{1}{2.5} = 0.4 , \text{Hz}
     ]

8. FAQs / Common Misconceptions

Q1: Is distance the same as displacement in rectilinear motion?
❌ No. Distance is the total path length; displacement is the shortest straight-line distance from the initial to final position.

Q2: Why is angular displacement considered dimensionless?
✅ Because it is defined as the ratio [ \theta = \dfrac{s}{r} ], and both [ s ] and [ r ] have the same unit of length.

Q3: Can a motion be both rectilinear and oscillatory?
✅ Yes. A ball oscillating horizontally on a frictionless straight track is both rectilinear (straight path) and oscillatory (back and forth).

Q4: What is the relation between angular velocity and linear velocity?

[
v = r\omega
]

Q5: Is oscillatory motion always periodic?
❌ Not necessarily. A motion can be oscillatory without being perfectly periodic if its restoring force is irregular.