HL Physics - Rigid Body Mechanics

Moment of Inertia

a measure of the ability of a body to resist changes in its rotational motion, depending on the mass distribution relative to the axis of rotation

Centripetal Acceleration

the acceleration caused by centripetal force, directed towards the center of the circular path

Angular Acceleration (α)

the rate of change of angular velocity over time (α = Δω / Δt)

Kinetic Energy of a Rolling object (THIS IS IMPORTANT TO REMEMBER)

if it is rolling it has both linear and rotational motion, so it has rotational and translational KE

Torque (τ)

a measure of the turning effect of a force (only occurs when the force is applied at an angle)

Rotational Equilibrium

a state where the sum of all torques acting on a body is zero, resulting in no net rotational motion

Angular Momentum

the product of a body's moment of inertia and its angular velocity (L = Iω)

Conservation of Angular Momentum

if no external torque acts on a system, the total angular momentum remains constant

Angular Impulse

the change in angular momentum of a body, caused by a resultant torque

Relating Linear Velocity and Angular Velocity

v = ωr (linear velocity = angular velocity x radius)

Kinetic Energy of a Rolling Object Formula

KE = (1/2mv²) + (1/2 x I x ω²)

Couple

pairs of equal and opposite forces on either side of a pivot with the same θ (produces rotational motion without translational motion)

Area on a Torque x Time Graph

area = angular impulse

Sign/Ladder Problem

1. Draw a free body diagram

2. Equate horizontal and vertical forces

3. Calculate the moments about a point (pick the point with the most forces acting on it, because they don't provide torque and can be ignored)

4. Solve for whatever value you are finding

5. You can substitute into the vertical and horizontal equations made in step 2 if needed

Linear and Angular Acceleration Equation

α = a / r