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Classical Mechanics

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Classical Mechanics

Parallel Axis Theorem

A theorem stating that the moment of inertia about any axis parallel to a centroidal axis equals the centroidal moment of inertia plus mass…

I = I_cm + M d² kg·m²
Classical Mechanics

Pascal's Principle

The principle stating that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and container…

ΔP = F1 / A1 = F2 / A2 Pa
Classical Mechanics

Period

The time duration required to complete one full cycle of a recurring motion or oscillation.

T = 1 / f = 2π / ω = 2π √(m/k) s
Classical Mechanics

Perpendicular Axis Theorem

A theorem stating that for a thin planar lamina, the moment of inertia about an axis perpendicular to the plane equals the sum of moments…

Iz = Ix + Iy kg·m²
Classical Mechanics

Potential Energy

The stored energy an object possesses due to its relative position in a conservative force field or its structural deformation.

PE_grav = m g h, PE_elastic = ½ k x² J
Classical Mechanics

Power

The rate at which work is performed or energy is transferred per unit time.

P = dW/dt = F · v W (J/s)
Classical Mechanics

Projectile Motion

The 2D motion of an object launched into a gravitational field under the sole influence of gravity (ignoring air resistance).

x(t) = v0 cos θ t, y(t) = v0 sin θ t - ½ g t² m, m/s