Motion in a Plane

Scalars have only magnitude (mass

Scalars have only magnitude (mass, temperature, speed), while vectors have both magnitude and direction (displacement, velocity, acceleration, force).

Vector addition follows parallelogram law

Vector addition follows parallelogram law: R⃗ = A⃗ + B⃗ with magnitude |R⃗| = √(A² + B² + 2AB cosθ). Triangle law states vectors form triangle sides.

Position vector r⃗ = xî +

Position vector r⃗ = xî + yĵ locates a point from origin. Displacement Δr⃗ = r⃗' - r⃗ = Δxî + Δyĵ represents change in position. Velocity v⃗ = Δr⃗/Δt

Motion under constant gravitational acceleration

Motion under constant gravitational acceleration with independent horizontal and vertical components. Initial velocity components: ux = u cosθ, uy = u

Motion with constant speed v along

Motion with constant speed v along circular path of radius r. Though speed is constant, velocity changes direction continuously, causing centripetal a