Power is how quickly work is done — work per unit time.

In absence of external forces, the total momentum before and after impact is the same.

It’s the stored energy a body possesses due to its height or configuration

Kinetic energy depends on mass and square of velocity.

Positive work means energy transfer in the direction of motion.

Impulse = Force × time = change in linear momentum.

Range is maximum when sin2θ = 1, which happens at θ = 45°.

Vertical motion equation gives the maximum height reached at topmost point.

Range depends on initial velocity, angle, and gravitational acceleration.

Time of flight depends on vertical component of velocity and gravity.

A projectile follows a parabolic path due to the combined horizontal and vertical motion.

Under gravity alone, a body falls with constant acceleration g.

Standard acceleration due to gravity is taken as 9.81 m/s² near Earth’s surface.

This equation relates final velocity, initial velocity, acceleration, and displacement.

The integral of acceleration with respect to time gives velocity change.

Integrating velocity over time gives total displacement.

The rate of change of velocity with time is acceleration.

The rate of change of displacement with respect to time is velocity.

Kinetics explains why motion occurs — relating force and mass to acceleration.

Kinematics studies the geometry of motion — displacement, velocity, and acceleration — without involving force.

Due to symmetry, the centroid always lies along the axis that divides the shape evenly.

In symmetrical figures, cross-products cancel out, making product of inertia zero.

A quarter circle’s centroid lies symmetrically at equal distances 4r/(3π) from the axes.

For a wire (line), the centroid is at 2r/π from the base along the axis of symmetry.

Using the parallel axis theorem, I = I₉ + m r² = (1/2 + 1/4) m r² = (3/4) m r².

It represents the distance from the axis where the entire mass can be assumed concentrated to give the same I.

Since k = √(I/m), the unit of radius of gyration is the same as length — meters.

It is valid only for flat laminae where Iₖ = Iₓ + Iᵧ.

The moment of inertia about any parallel axis equals that about centroidal axis plus m h².

Since all mass is at the outer radius, I = m r² for a thin hollow cylinder.

For a solid cylinder, I = ½ m r² about its central longitudinal axis.

Shifting the axis from center to end using the parallel axis theorem gives I = (1/3) mL².

Using standard formulas, I = (1/12) mL² for a uniform rod rotating about its center.

It combines mass and the square of distance from the axis, hence its unit is kg·m².

It measures how mass is distributed relative to an axis, resisting rotational motion.

In a right triangle, the centroid divides the medians in a 2:1 ratio, giving one-third distances from sides.

Because a circle is perfectly symmetrical, its geometric center is also the centroid.

The diagonals of a rectangle intersect at its center, which is also its centroid.

For a semicircle, the centroid is located along the axis of symmetry at 4r/3π from the flat edge.

The centroid is the point where all three medians of a triangle meet, dividing each in a 2:1 ratio.

Friction always acts opposite to the direction of relative motion between surfaces.

The angle of repose is where limiting friction equals component of weight parallel to the plane.

Using vector addition, resultant = √(F² + F²) = √2F.

Rougher surfaces increase friction, smoother ones reduce it.

Without friction, there’s no resistance — the body moves effortlessly.

It’s a ratio of two forces, hence has no units or dimensions.

Both angles represent the same condition at which motion just begins.

Kinetic (sliding) friction opposes motion after movement begins.

Static friction is stronger — once motion starts, friction drops to kinetic level.

The rotational balance condition requires the sum of all moments to be zero.

At the verge of motion, static friction reaches its maximum — the limiting friction.

It’s the ratio of frictional force to normal reaction, a measure of surface roughness.

It’s the greatest static friction value just before the body begins to move.

The angle of friction shows how much resistance exists between two surfaces in contact.

Friction resists motion, always opposing the direction of relative movement.

It applies to multiple concurrent forces forming a closed polygon when in equilibrium.

Three forces in equilibrium must be concurrent and follow the triangle or Lami’s law.

Concurrent forces act at a single point, maintaining balance through that common intersection.

For complete equilibrium, both total force and total moment must be zero.

When all forces cancel each other, the net (resultant) force becomes zero — that’s equilibrium.

Equal, opposite, and collinear forces cancel each other perfectly.

Zero resultant means balanced forces — no acceleration, hence equilibrium.

The resultant is the vector addition of all applied forces.

The parallelogram law gives both magnitude and direction of the resultant.

That point is the rotational reference where moments balance.

Equal and opposite forces cancel out completely.

General system means forces act in different directions, not meeting at one point.

The line of action represents the straight line along which the force acts.

Equal and opposite non-collinear forces form a couple, causing rotation.

The polygon law helps determine the resultant of multiple concurrent forces.

Lami’s theorem applies when three forces keep a body in equilibrium.

“Coplanar parallel” means all forces lie in the same plane and are parallel.

Resultant of concurrent forces passes through their intersection point.

Equal and opposite forces cancel each other out.

Moment of couple = Force × arm distance.

A couple creates pure rotational motion without translation.

It applies to forces acting at a single point and at an angle to each other.

By Pythagoras theorem, resultant R = √(F² + F²) = F√2.

When R = F, using the law of parallelogram gives cosθ = -½ → θ = 120°.

A system of forces exists when multiple forces act simultaneously on one body.

Dynamics focuses on moving bodies and the forces causing that motion.

1 kilogram-force = weight of 1 kg mass under gravity (9.81 m/s²).

1 Newton = 1 kg·m/s² as per F = m·a.

Impulse = Force × Time, which has the same unit as momentum (N·s).

The area gives total displacement covered during motion.

Velocity is the rate at which displacement changes with time.

Work has magnitude only, not direction, so it’s a scalar quantity.

Moment is force × perpendicular distance, so its unit is newton-metre (N·m).

A force’s external effect on a rigid body remains the same along its line of action.

Mechanics deals with motion, forces, and their effects on bodies.

Force equals the time rate of change of momentum.

Inertia is a body’s natural tendency to resist any change in its motion.

Force is the product of mass and acceleration, according to Newton’s second law.

In mechanics, rigid bodies are assumed not to deform under applied forces.

Center of gravity is the point where the body’s entire weight acts vertically downward

Every force has an equal and opposite counter-force — Newton’s third law.

Newton’s second law relates force, mass, and acceleration (F = m·a).

The first law of motion defines inertia — the tendency to resist changes in motion.

Force is measured in newtons (N), where 1 N = 1 kg·m/s².

Newton gave three laws of motion — gravitation is a separate law discovered later by him.