ECAT Physics Syllabus

State the first condition of equilibrium.

The vector sum of all forces acting on a body is zero: ΣF = 0 (ΣFₓ = 0 and ΣFᵧ = 0).

State the second condition of equilibrium.

The sum of all torques (moments) acting on the body about any point is zero: Στ = 0.

Define torque and give its formula.

Torque is the turning effect of a force about a pivot: τ = r F sin θ, where r is the moment arm distance and θ the angle between r and F.

Differentiate between distance and displacement.

Distance is the total path length travelled (scalar). Displacement is the straight-line change in position from start to end with direction (vector).

Define instantaneous velocity and instantaneous acceleration.

Instantaneous velocity is the rate of change of displacement at an instant (limit of Δs/Δt as Δt→0). Instantaneous acceleration is the rate of change of velocity at an instant.

State the three equations of motion for uniform acceleration.

v = u + at; s = ut + ½at²; v² = u² + 2as.

For a body in free fall (taking down as positive), what value of acceleration is used and what is the velocity equation?

a = g ≈ 9.8 m/s²; v = u + gt, with u = 0 if dropped from rest.

On a velocity–time graph, what do the slope and the area under the line represent?

The slope represents acceleration; the area under the line represents displacement.

State Newton's first law of motion.

A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force (law of inertia).

State Newton's second law of motion and its equation.

The net force on a body equals the rate of change of its momentum; for constant mass, F = ma.

State Newton's third law of motion.

For every action there is an equal and opposite reaction; forces between two bodies are equal in magnitude and opposite in direction.

Define inertia and state what it depends on.

Inertia is a body's resistance to any change in its state of motion; it depends directly on the body's mass.

What is the difference between mass and weight?

Mass is the quantity of matter (scalar, constant, kg). Weight is the gravitational force on the mass (vector, W = mg, newtons, varies with g).

Define linear momentum and give its formula and SI unit.

Momentum is the product of mass and velocity: p = mv. SI unit: kg·m/s. It is a vector.

Define impulse and state the impulse–momentum theorem.

Impulse = force × time of contact (J = F·t). The impulse–momentum theorem states impulse equals the change in momentum: F·t = Δp = m(v − u).

State the law of conservation of linear momentum.

In the absence of an external net force, the total momentum of a system remains constant before and after a collision/interaction.

Differentiate between elastic and inelastic collisions.

In an elastic collision both momentum and kinetic energy are conserved. In an inelastic collision momentum is conserved but kinetic energy is not (some converts to other forms).

What is a perfectly inelastic collision?

A collision in which the colliding bodies stick together and move with a common velocity afterward; momentum is conserved but maximum kinetic energy is lost.

Define projectile motion.

The two-dimensional motion of a body projected near Earth's surface that moves under gravity alone, following a parabolic path (neglecting air resistance).

For a projectile launched at speed v at angle θ, what are the horizontal and vertical components of initial velocity?

Horizontal: vₓ = v cos θ (constant). Vertical: vᵧ = v sin θ (changes due to gravity).

Give the formula for the time of flight of a projectile launched at angle θ on level ground.

T = (2 v sin θ) / g.

Give the formula for the maximum height of a projectile.

H = (v² sin²θ) / (2g).

Give the formula for the horizontal range of a projectile and the angle for maximum range.

R = (v² sin 2θ) / g; maximum range occurs at θ = 45°.

Why is the horizontal velocity of a projectile constant while the vertical velocity changes?

No horizontal force acts (ignoring air resistance), so horizontal velocity is constant; gravity acts vertically, continuously changing the vertical velocity.

Define work done by a constant force and give its general formula.

Work is the product of force and displacement in the direction of the force: W = F·d·cos θ, where θ is the angle between F and d. SI unit: joule (J).

When is the work done by a force zero, positive, and negative?

Zero when θ = 90° (force perpendicular to displacement); positive when θ < 90°; negative when θ > 90° (force opposes motion).

Define kinetic energy and give its formula.

Kinetic energy is the energy a body possesses due to its motion: KE = ½mv². SI unit: joule.

Define gravitational potential energy and give its formula near Earth's surface.

The energy stored in a body due to its position/height: PE = mgh, where h is height above a reference level.

State the work–energy theorem.

The net work done on a body equals the change in its kinetic energy: W_net = ΔKE = ½mv² − ½mu².

State the law of conservation of energy.

Energy can neither be created nor destroyed, only transformed from one form to another; the total energy of an isolated system remains constant.

Define power, give its formula, SI unit, and the relation P = Fv.

Power is the rate of doing work: P = W/t. SI unit: watt (W = J/s). For a force moving at constant velocity, P = Fv.

Define efficiency and give its formula as a percentage.

Efficiency = (useful output energy or power ÷ total input energy or power) × 100%. It is always less than 100% due to energy losses.

Define angular displacement and give its SI unit; how do you convert degrees to radians?

Angular displacement is the angle swept by a rotating body, measured in radians (rad). 1 radian = 180/π ≈ 57.3°; radians = degrees × (π/180). Also θ = s/r (arc length over radius).

Define angular velocity, give its formula and the relation between linear and angular velocity.

Angular velocity ω is the rate of change of angular displacement: ω = θ/t (rad/s). Linear and angular velocity relate by v = rω.

Give the relation between linear acceleration and angular acceleration, and the formula for ω in terms of period T or frequency f.

a = rα (tangential). Angular velocity ω = 2π/T = 2πf, where T is the period and f the frequency of rotation.