PRELIMS

02. Motion and Mechanics

1. Scalar, Vector & Tensor Quantities

• Scalar Quantities: Physical quantities which have magnitude only and no direction.
  • Examples: Mass, speed, volume, work, time, power, energy, etc.
• Vector Quantities: Physical quantities which have magnitude and direction both and which obey triangle law.
  • Examples: Displacement, velocity, acceleration, force, momentum, torque, etc.
• Special Case: Electric Current: Although it has a direction, it is a scalar quantity because it does not obey the triangle law of addition.
• Tensor Quantities: Moment of inertia, pressure, refractive index, stress.

2. Distance and Displacement

• Distance: Length of the actual path covered by a moving object in a given time interval. Scalar; always positive.
• Displacement: Shortest distance covered by a body in a definite direction. Vector; may be positive, negative, or zero.
• Relationship: .

3. Speed, Velocity and Acceleration

• Speed: Distance travelled in unit time ( ). Scalar; SI unit: .
• Velocity: Displacement in unit time ( ). Vector; SI unit: .
• Acceleration: Rate of change of velocity ( ). Vector; SI unit: .
  • Retardation: Negative acceleration (when velocity decreases with time).

4. Circular & Angular Motion

• Circular Motion: Motion along a circular path. Uniform circular motion is an accelerated motion because the direction of velocity changes continuously.
• Angular Velocity ( ): Angle subtended by the line joining the object from the origin of the circle in unit time ( ).
  • Relationship: (Linear speed = Angular speed Radius).
  • Time Period ( ) & Frequency ( ): and .

5. Newton's Laws of Motion

Established by Newton in his book "Principia" (1687).

• First Law of Motion (Law of Galileo/Inertia): Every body maintains its initial state of rest or uniform motion unless an external force acts on it.
  • Inertia: Property by which a body opposes change in its initial state.
  • Examples of Inertia:
    1. Passengers bend backward when a car starts suddenly.
    2. Rider bends forward when a horse stops suddenly.
    3. Dust is removed from a coat/blanket when beaten with a stick.
  • Note: First law gives the definition of force.
• Second Law of Motion: The rate of change in momentum is directly proportional to the applied force.
  • Force ( ): ( ).
  • Momentum ( ): . Vector; SI unit: .
  • Note: Second law gives the magnitude of force.
• Third Law of Motion: To every action, there is an equal and opposite reaction.
  • Examples: Recoil of a gun, motion of a rocket, swimming, pulling water from a well (falling back if the rope breaks).

6. Impulse & Momentum Principles

• Principle of Conservation of Linear Momentum: If no external force acts on a system of bodies, the total linear momentum remains constant ( ).
• Impulse: When a large force acts for a very small time. . Vector; SI unit: .

7. Centripetal & Centrifugal Forces

• Centripetal Force: Force acting towards the centre to maintain circular motion ( ).
• Centrifugal Force: A pseudo force (inertial force) equal and opposite to centripetal force.
  • Applications: Cream separator, centrifugal drier.

8. Moment of Force, CG & Equilibrium

• Moment of Force: Rotational effect about an axis ( ). Vector; SI unit: .
• Centre of Gravity (CG): Point through which the entire weight of the body acts.
• Equilibrium: Resultant of all forces is zero.
  • Stable: Body regains position after slight displacement (CG is at minimum height).
  • Unstable: Body moves further after displacement (CG is at highest position).
  • Neutral: Body stays in new position (CG remains at same height).
• Conditions for Stable Equilibrium:
  1. CG should be at the minimum height.
  2. Vertical line through CG must pass through the base of the body.

9. Types of Motion & Equations of Uniformly Accelerated Motion

• Translatory Motion: Rectilinear (straight line) or Curvilinear (curved path).
• Rotatory Motion: Motion about a fixed axis.
• Periodic/Oscillatory Motion: Motion that repeats itself at regular time intervals.
• Equations of Motion (for constant acceleration , initial velocity , final velocity , time , displacement ):

10. Commonly Confused Pairs

• Mass vs. Weight:
  • Mass: Quantity of matter in a body; scalar; SI unit kg; constant everywhere (measured by a beam/pan balance).
  • Weight: Force with which a body is attracted towards the Earth ( ); vector; SI unit newton; varies with (measured by a spring balance).
• Speed vs. Velocity: Speed is distance/time (scalar, always positive); Velocity is displacement/time (vector, can be zero/negative even if speed is not).
• Momentum vs. Impulse: Momentum ( ) is the state of motion at an instant; Impulse ( ) is the change produced in momentum over an interval.
• Centripetal vs. Centrifugal: Centripetal is a real force acting towards the centre; Centrifugal is a pseudo/fictitious force experienced in a rotating (non-inertial) frame, directed away from the centre.

UPSC Relevance

• Inertia: Qualitative questions on "why things happen" (bus starting/stopping).
• Conservation of Momentum: Rocket propulsion is a frequently asked concept.
• Forces: Distinguishing centripetal/centrifugal in devices like washing machines or separators.
• Confused Pairs: Mass vs. Weight and Speed vs. Velocity are classic single-line MCQ traps.