Physics Mechanics Notes for SSC Exams

Mechanics forms the base of Physics and appears in every SSC General Science section in the form of direct questions on units, laws of motion, gravitation, work-energy-power and fluids. These notes cover the SSC-level mechanics syllabus chapter by chapter with formulas, comparison tables and solved examples. Learn the units and definitions first and the formulas next, as a Physics teacher would advise.

Scalar and Vector Quantities

Motion in a Straight Line

• Distance: total path length, scalar. Displacement: shortest distance from the initial to the final position, vector.
• Speed = distance / time (unit m/s). Velocity = displacement / time. Acceleration = change in velocity / time (unit m/s squared). Negative acceleration is called retardation or deceleration.
• Uniform motion: equal distances in equal intervals of time. Non-uniform: unequal distances.
• Average speed = total distance / total time. Average velocity = total displacement / total time.

Equations of Motion (uniform acceleration)

• For a freely falling body: u = 0 and a = g = 9.8 m/s squared. Time of fall from height h is the square root of (2h/g).
• In the x-t graph, slope = velocity. In the v-t graph, slope = acceleration and area = displacement.

Circular Motion and Projectile

• In uniform circular motion the speed is constant but the direction (and therefore velocity) keeps changing, so there is an acceleration directed to the centre, called the centripetal acceleration = v squared / r. Centripetal force = m v squared / r.
• The centrifugal force is a pseudo force acting away from the centre in the rotating frame. Cream separators and washing-machine dryers work on it.
• A projectile moves under gravity along a parabola. Range R = u squared sin(2 theta) / g. The range is maximum at an angle of 45 degrees. Time of flight = 2 u sin(theta) / g.
• Two projection angles that add to 90 degrees give the same range.

Newton's Laws of Motion

• Momentum p = mv (unit kg m/s). Impulse = force x time = change in momentum.
• Conservation of momentum: total momentum before collision = total momentum after, if no external force acts.
• SI unit of force: newton (1 N = 1 kg m/s squared). CGS unit: dyne (1 N = 10^5 dyne).

Friction

• Friction is the force that opposes the relative motion between two surfaces in contact. It acts opposite to the direction of motion.
• Types: static friction (before motion) > kinetic or sliding friction > rolling friction. Rolling friction is the smallest, which is why wheels are used.
• Limiting friction f = mu x N, where mu is the coefficient of friction and N the normal reaction. It does not depend on the area of contact.
• Friction is a necessary evil: it helps us walk and brake but wastes energy and wears out machines. It is reduced by lubricants, ball bearings and streamlining.

Work, Energy and Power

• Work is zero when the force is perpendicular to the displacement (for example, a satellite moving in a circular orbit, or a person carrying a load on level ground).
• Work done by gravity on a body moving up is negative.
• Law of conservation of energy: energy can neither be created nor destroyed, only converted from one form to another.
• 1 horsepower (hp) = 746 watt. 1 kilowatt-hour (kWh) = 1 unit of electricity = 3.6 x 10^6 joule. 1 calorie = 4.186 joule.

Gravitation

• Newton's law of gravitation: F = G m1 m2 / r squared. G (universal gravitational constant) = 6.67 x 10^-11 N m squared / kg squared, measured by Cavendish.
• Acceleration due to gravity g = G M / R squared = 9.8 m/s squared. It is maximum at the poles, minimum at the equator, decreases with altitude and with depth, and is zero at the centre.
• Mass vs weight: mass is constant, weight W = m g changes. Weight is zero in free fall and at the centre of the Earth. The weight on the Moon is about 1/6 of that on the Earth because g on the Moon is about 1.63 m/s squared.
• Escape velocity = square root of (2 g R) = 11.2 km/s for the Earth. Orbital velocity near the Earth = 7.9 km/s.
• Kepler's laws: (1) planets move in elliptical orbits with the Sun at one focus, (2) the line joining a planet and the Sun sweeps equal areas in equal times, (3) T squared is proportional to r cubed.
• Satellites: a geostationary satellite has a time period of 24 hours, moves west to east above the equator at a height of about 36,000 km. Polar satellites orbit at 500 to 800 km.
• Weightlessness is felt by astronauts in an orbiting satellite because they are in free fall.

Pressure and Fluids

• A body floats if its density is less than that of the liquid. Ice floats on water since it is less dense and 1/10 of it remains above the surface.
• Viscosity is the internal friction of a fluid (honey is more viscous than water). Surface tension makes water droplets spherical and allows insects to walk on water. Capillarity is the rise of liquid in a thin tube (oil rising in a lamp wick).
• Soaps and detergents reduce surface tension.

Elasticity and Simple Harmonic Motion

• Hooke's law: within the elastic limit, stress is proportional to strain. Young's modulus = stress / strain.
• Steel is more elastic than rubber. A body that regains its original shape on removing the force is called perfectly elastic.
• Time period of a simple pendulum T = 2 pi times the square root of (l/g). It does not depend on the mass of the bob, and a pendulum clock runs slow at higher altitudes or on the Moon. A seconds pendulum has a time period of 2 seconds (length about 99.4 cm).

Rotational Motion

• Moment of inertia is the rotational equivalent of mass. Torque = force x perpendicular distance (unit N m). Angular momentum = moment of inertia x angular velocity.
• A figure skater spins faster by pulling the arms in because the moment of inertia decreases (conservation of angular momentum).
• The centre of mass of a uniform body lies at its geometric centre. A body is in stable equilibrium if its centre of gravity is low and its base is wide.

Units and Quick Revision

Practice Questions With Answers

1. Which law of motion is known as the law of inertia? Answer: Newton's first law
2. The SI unit of power is: Answer: Watt
3. Where is the value of g maximum on the Earth? Answer: At the poles
4. At what angle is the range of a projectile maximum? Answer: 45 degrees
5. Which type of friction is the least? Answer: Rolling friction
6. The escape velocity of the Earth is: Answer: 11.2 km/s
7. Hydraulic brakes work on which law? Answer: Pascal's law
8. What is the work done by a satellite moving in a circular orbit? Answer: Zero
9. The SI unit of momentum is: Answer: kg m/s
10. Who measured the value of G? Answer: Henry Cavendish

Continue with the Heat and Thermodynamics notes and practise with our previous year question papers.

Frequently Asked Questions

What is mechanics in Physics?

Mechanics is the branch of Physics that deals with the motion of bodies and the forces that cause or change the motion. It has two parts: kinematics (study of motion without its causes) and dynamics (study of motion with the forces that cause it).

What is the difference between distance and displacement?

Distance is the total path length covered by a body and is a scalar that is always positive. Displacement is the shortest straight-line distance between the initial and final positions with direction; it is a vector and can be positive, negative or zero.

What is the difference between speed and velocity?

Speed is the rate of change of distance (scalar), while velocity is the rate of change of displacement (vector). A body moving in a circle at constant speed has a changing velocity.

What are the three equations of motion?

For uniform acceleration: v = u + at, s = ut + (1/2)at squared, and v squared = u squared + 2as, where u is the initial velocity, v the final velocity, a acceleration, t time and s displacement.

What do the slopes of motion graphs tell us?

The slope of a position-time graph gives velocity, the slope of a velocity-time graph gives acceleration, and the area under a velocity-time graph gives displacement.

State Newton's three laws of motion.

First law (inertia): a body continues in its state of rest or uniform motion unless acted upon by an external force. Second law: force equals the rate of change of momentum, F = ma. Third law: to every action there is an equal and opposite reaction.

What is inertia?

Inertia is the tendency of a body to resist a change in its state of rest or of uniform motion. Mass is the measure of inertia. A passenger falls forward when a moving bus stops suddenly because of inertia.

What is the difference between mass and weight?

Mass is the quantity of matter in a body, is constant everywhere and is measured in kg. Weight is the force with which the Earth attracts a body (W = mg), changes with place and is measured in newton. A body weighs about one sixth on the Moon compared with the Earth.

What is the law of conservation of momentum?

In the absence of an external force, the total momentum of a system remains constant. It explains the recoil of a gun and the working of rockets.

What is the SI unit of work, power and energy?

Work and energy are measured in joule (J), and power is measured in watt (W). 1 horsepower is equal to 746 watt and 1 kilowatt-hour is equal to 3.6 x 10^6 joule.

What is the work-energy theorem?

The work done by the net force on a body is equal to the change in its kinetic energy. Kinetic energy is (1/2)mv squared and gravitational potential energy is mgh.

What is the universal law of gravitation?

Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G m1 m2 / r squared, where G = 6.67 x 10^-11 N m squared per kg squared.

Where is the value of g maximum and minimum on the Earth?

The acceleration due to gravity g is maximum at the poles (about 9.83 m/s squared) and minimum at the equator (about 9.78 m/s squared). It also decreases with height and with depth below the surface, and it is zero at the centre of the Earth.

What are escape velocity and orbital velocity of the Earth?

Escape velocity is about 11.2 km/s, the minimum speed needed to leave the Earth's gravity. Orbital velocity near the surface is about 7.9 km/s.

What is Archimedes' principle?

When a body is wholly or partly immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced. A body floats if its density is less than that of the fluid. Ships float for this reason.

Which Mechanics topics are asked in SSC exams?

Scalar and vector quantities, equations of motion, Newton's laws, friction, work-energy-power, gravitation, circular motion, pressure, Pascal's law and Archimedes' principle, simple pendulum and units. These notes cover them all.