JEE Mains Physics: Mechanics Formulas Flashcards

Question 1

Define v = u + at.

Accepted Answer

The first equation of motion gives final velocity from initial velocity, constant acceleration and time, and it holds only while acceleration stays constant.

Question 2

Define s = ut + ½at².

Accepted Answer

The second equation of motion gives displacement from initial velocity, constant acceleration and elapsed time, without needing the final velocity at all.

Question 3

Define v² = u² + 2as.

Accepted Answer

The third equation of motion links velocities, acceleration and displacement with no time term, which makes it the fastest route when time is not given.

Question 4

Define Displacement in the nth Second.

Accepted Answer

The relation s = u + a(2n − 1)/2 gives the distance covered during the nth second alone, assuming motion in one direction under constant acceleration.

Question 5

Define Time of Flight.

Accepted Answer

The relation T = 2u sinθ / g gives the total time a projectile spends in the air when it lands at the same level from which it was launched.

Question 6

Define Maximum Height of a Projectile.

Accepted Answer

The relation H = u² sin²θ / 2g gives the greatest height above the launch point, set entirely by the vertical component of the launch velocity.

Question 7

Define Horizontal Range.

Accepted Answer

The relation R = u² sin2θ / g gives the horizontal distance covered on level ground, and it is greatest at a launch angle of 45 degrees for a fixed speed.

Question 8

Define Equation of Trajectory.

Accepted Answer

The relation y = x tanθ − gx² / (2u² cos²θ) describes a projectile's parabolic path by giving its height at any horizontal distance from launch.

Question 9

Define Relative Velocity.

Accepted Answer

The vector v_AB = v_A − v_B gives the velocity of A as seen by an observer moving with B, found by subtracting vectors rather than their magnitudes.

Question 10

Define Newton's Second Law.

Accepted Answer

The law F = dp/dt states that net force equals the rate of change of momentum, which reduces to F = ma when the mass stays constant.

Question 11

What is Impulse?

Accepted Answer

The quantity J = FΔt = Δp is the product of a force and its duration, and it equals the change in momentum that force produces on a body.

Question 12

Define Limiting Static Friction.

Accepted Answer

The relation f ≤ μₛN means static friction adjusts to match the applied force, but only up to a maximum set by the coefficient and the normal reaction.

Question 13

Define Kinetic Friction.

Accepted Answer

The relation f = μₖN gives the friction force on a sliding surface, usually smaller than limiting static friction and largely independent of the contact area.

Question 14

Define Angle of Repose.

Accepted Answer

The relation tanθ = μₛ defines the steepest incline angle on which a block stays at rest without slipping, independent of the mass of the block.

Question 15

Define Centripetal Force.

Accepted Answer

The expression F = mv²/r gives the net inward force needed to keep a body of mass m moving at speed v around a circle of radius r.

Question 16

Define Banking Angle.

Accepted Answer

The relation tanθ = v²/rg gives the bank angle at which a vehicle takes a curve at speed v with no friction needed from the road surface.

Question 17

Define Work Done by a Constant Force.

Accepted Answer

The expression W = Fs cosθ is the dot product of force and displacement, where θ is the angle between those two vectors throughout the motion.

Question 18

Define Work-Energy Theorem.

Accepted Answer

The net work done by all forces acting on a body equals the change in its kinetic energy, whether those forces are constant or varying.

Question 19

Define Elastic Potential Energy.

Accepted Answer

The expression U = ½kx² is the energy stored in an ideal spring of stiffness k when it is stretched or compressed a distance x from natural length.

Question 20

What is Power?

Accepted Answer

The expression P = dW/dt = F·v is the rate of doing work, and its instantaneous form equals the dot product of force and velocity at that moment.

Question 21

Define Coefficient of Restitution.

Accepted Answer

The ratio e equals relative speed of separation over relative speed of approach along the line of impact, from 0 for perfectly inelastic to 1 for elastic.

Question 22

Define Centre of Mass.

Accepted Answer

The position x_cm = Σmᵢxᵢ / Σmᵢ is the mass-weighted average position of a system, the point that moves as if all external force acted there.

Question 23

Define Moment of Inertia.

Accepted Answer

The quantity I = Σmr² measures a body's resistance to angular acceleration about a chosen axis, depending on its mass and how far that mass sits from the axis.

Question 24

Define Parallel Axis Theorem.

Accepted Answer

The relation I = I_cm + Md² gives the moment of inertia about any axis parallel to one through the centre of mass, at perpendicular distance d.

Question 25

Define Perpendicular Axis Theorem.

Accepted Answer

The relation I_z = I_x + I_y applies only to flat laminar bodies, where x and y lie in the plane and z is perpendicular, all meeting at one point.

Question 26

What is Torque?

Accepted Answer

The vector τ = r × F is the turning effect of a force, with magnitude rF sinθ where θ is the angle between the position vector and the force.

Question 27

Define Angular Momentum of a Rigid Body.

Accepted Answer

The quantity L = Iω applies to a rigid body about a fixed axis, and it is conserved whenever the net external torque about that axis is zero.

Question 28

Define Kinetic Energy of Rolling.

Accepted Answer

The expression KE = ½mv²(1 + k²/R²) is the total kinetic energy of a body rolling without slipping, combining translation and rotation through its radius of gyration k.

Question 29

Define Acceleration While Rolling Down an Incline.

Accepted Answer

The relation a = g sinθ / (1 + k²/R²) gives the acceleration of a body rolling without slipping, so a smaller k²/R² produces a larger acceleration.

Question 30

Define Newton's Law of Gravitation.

Accepted Answer

The relation F = Gm₁m₂/r² gives the attractive force between two point masses, proportional to each mass and inversely proportional to the square of their separation.

Question 31

Define Gravity at Height h.

Accepted Answer

The relation g_h = g(1 + h/R)⁻² gives gravitational acceleration at height h above a planet's surface, simplifying to g(1 − 2h/R) when h is much smaller than R.

Question 32

Define Orbital Velocity.

Accepted Answer

The speed v = √(GM/r) keeps a satellite in a circular orbit of radius r, and close to Earth's surface it is approximately 7.9 km/s.

Question 33

Define Escape Velocity.

Accepted Answer

The speed vₑ = √(2GM/R) is the minimum launch speed needed to leave a planet's gravity without further thrust, about 11.2 km/s for Earth.

Question 34

Define Kepler's Third Law.

Accepted Answer

The relation T² ∝ r³ states that the square of an orbital period is proportional to the cube of the orbit's semi-major axis around one central mass.