Chapter 8 Physics Notes!

Rotational Inertia / Moment of Inertia

Quantifies an object's resistance to change in its rotational motion; depends on mass and mass distribution relative to axis.

Torque

The tendency of a force to cause an object to rotate about an axis

Inertia

an object’s tendency to resist changes to its state of motion.

Rotational Equilibrium

A state where the net torque on an object is zero, resulting in no rotational motion.

Translational Equilibrium

A state of balanced forces where the net force acting on an object is zero.

Static Equilibrium

The condition when an object remains at rest.

Newton's Second Law (Rotational)

Translates to τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

Clockwise Torque

Defined as negative torque; occurs when force causes rotation in a clockwise direction.

Counter-Clockwise Torque

Defined as positive torque; occurs when force causes rotation in a counter-clockwise direction.

Effect of Mass Distribution

Higher mass positioned further from the rotation axis results in greater rotational inertia.

Equation for how to find α

α = a/r

Equation for how to find a

a = 2x/t²

Equation for how to find torque (with inertia)

τ = Iα

Equation for how to find torque (without inertia)

τ = Fr sinθ

Equation for how to find inertia (with no disk)

I = Σmr²

Equation for how to find inertia (with disk)

I = ½Mr²