IIT JAM Physics key terms

A measure of how mass is distributed about an axis, equal to the sum of each mass element times the square of its distance from that axis; it plays the role of mass in rotational motion.

Relates the moment of inertia about any axis to that about a parallel axis through the centre of mass: I equals I_cm plus mass times the square of the separation between the axes.

The rotational analogue of linear momentum, equal to the cross product of position and linear momentum, or to moment of inertia times angular velocity for a rigid body about a fixed axis.

The turning effect of a force about a point, given by the cross product of the position vector from that point to the force's point of application and the force itself.

When the net external torque on a system is zero, its total angular momentum stays constant; this underlies phenomena such as a figure skater speeding up on pulling in the arms.

A force on a particle that always points toward or away from a fixed point and whose magnitude depends only on distance from that point; such forces conserve angular momentum and are conservative.

Three empirical rules of planetary motion: orbits are ellipses with the Sun at one focus; the radius vector sweeps equal areas in equal times; and the square of the period is proportional to the cube of the semi-major axis.

The minimum speed needed at a given point for a body to escape a gravitational field to infinity without further propulsion; for Earth from the surface it is about 11.2 kilometres per second.

The gravitational potential energy per unit mass at a point, conventionally taken as zero at infinity and negative at finite distance from a mass, equal to minus G times mass divided by distance.

A force for which the work done moving between two points is path-independent, so it can be written as the negative gradient of a scalar potential energy and the work around any closed loop is zero.

Oscillation in which the restoring force is directly proportional to displacement from equilibrium and directed oppositely, producing sinusoidal motion with a fixed angular frequency independent of amplitude.

Oscillatory motion in which a velocity-dependent resistive force gradually reduces amplitude; depending on strength of damping the system may be underdamped, critically damped, or overdamped.

The large-amplitude response of a driven oscillator when the driving frequency approaches its natural frequency; damping limits the peak amplitude and shifts it slightly below the undamped natural frequency.

A fictitious force experienced in a rotating reference frame, proportional to the velocity of a body in that frame and directed perpendicular to both the velocity and the rotation axis.

An outward fictitious force perceived in a rotating frame, equal in magnitude to mass times angular speed squared times distance from the rotation axis and directed away from that axis.

A reference frame in which a body with no net force applied moves with constant velocity; Newton's laws hold in their simple form only in such frames.

A symmetric second-rank tensor that generalises scalar moment of inertia, relating angular velocity vector to angular momentum vector for rotation about an arbitrary axis through a rigid body.

Three mutually perpendicular axes through a point for which the products of inertia vanish, so the inertia tensor is diagonal and angular momentum is parallel to angular velocity when rotation is about one of them.

In central-force motion, the sum of the true potential energy and the centrifugal term from angular momentum; its shape reveals whether orbits are bounded and where turning points occur.

A restatement of Newton's second law stating that the sum of applied forces and the reversed inertial force (mass times acceleration) does zero virtual work for any virtual displacement consistent with constraints.

Any set of independent variables that fully specify the configuration of a constrained system, chosen freely and fewer in number than Cartesian coordinates when constraints exist.

The difference between a system's total kinetic energy and its potential energy, expressed in generalised coordinates and velocities; its equation of motion follows from the Euler-Lagrange equations.

For conservative systems, the total energy written as a function of generalised coordinates and conjugate momenta; it generates the equations of motion and is conserved when it has no explicit time dependence.

A generalised coordinate that does not appear explicitly in the Lagrangian; its conjugate momentum is then conserved, a result known as Noether's theorem for this special case.

A principle linking every continuous symmetry of a system's action to a conserved quantity, for example time-translation symmetry to energy conservation and rotational symmetry to angular momentum conservation.

The framework in which the laws of physics are the same in all inertial frames and the speed of light in vacuum is invariant, leading to time dilation, length contraction, and mass-energy equivalence.

The set of linear equations relating space and time coordinates of the same event in two inertial frames moving at constant relative velocity; it reduces to the Galilean transformation at low speeds.

The effect in which a clock moving relative to an observer runs slow compared with the observer's own clocks, by the Lorentz factor; it is symmetric between inertial observers.

The time interval measured by a clock that travels between two events, i.e. in a frame where the events occur at the same place; it is the maximum interval and is invariant.

A set of four quantities that transforms under Lorentz transformations like the spacetime displacement; examples include energy-momentum and current density, whose squared norms are invariant.

The principle that matter and radiation exhibit both wave-like and particle-like behaviour depending on the experiment; for example electrons diffract like waves yet strike detectors as discrete particles.

Emission of electrons from a metal surface when light of sufficiently high frequency falls on it; the maximum kinetic energy depends on frequency, not intensity, supporting the photon model.

Elastic scattering of a photon by a free electron in which the photon loses energy and its wavelength increases by an amount depending on the scattering angle, confirming photon momentum.

The wavelength associated with a particle's motion, equal to Planck's constant divided by the magnitude of its momentum; it becomes significant for low-mass particles at low speeds.

A fundamental limit stating that certain pairs of observables, such as position and momentum, cannot both be known with arbitrary precision; the product of their uncertainties is at least h-bar over two.

A complex-valued function of position and time whose squared modulus gives the probability density of finding a particle at a location; it obeys the Schrodinger equation.

An equation of the form operator acting on a function equals a constant times that same function; the allowed constants are eigenvalues and correspond to possible measured values of the observable.

An operator equal to its own adjoint; it has real eigenvalues and orthogonal eigenfunctions, making it the mathematical representation of a physical observable in quantum mechanics.

The operator combination AB minus BA for two operators A and B; when it vanishes the observables can be measured simultaneously with arbitrary precision, otherwise they are subject to uncertainty relations.

A particle confined between impenetrable walls, whose allowed energies are quantised and proportional to the square of an integer; the model illustrates nodes, zero-point energy, and normalisation.

The minimum energy needed to remove an electron from the surface of a particular metal; in the photoelectric effect it equals the photon energy minus the maximum kinetic energy of emitted electrons.