Physics Chapter: Rotational Dynamics and Inertia

The consistent SI units are: meters (m) for length, radians (rad) for angular displacement, kilograms (kg) for mass, and seconds (s) for time.

I = t/a

<p>Thin hoop, radius R = MR² Thin hoop, radius R, width w = 1/2Mw² Solid cylinder, radius R, length l = 1/2MR² Long uniform rod, length l, through the center = 1/12ML² Hollow cylinder, inner radius R1, outer radius R2 = 1/2M(R1² + R2²) Uniform sphere, radius R = 2/5MR² Long uniform rod, length l, through one end = 1/3ML² Rectangular thin plate, length l, width w, through the center = 1/12M(l² + w²)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Newton's second law for rotation and Newton's second law for translation</p> Signup and view all the answers

Torque (τ) equals the moment of inertia (I) times the angular acceleration (α): τ = Iα.

A measure of an object's resistance to changes in its rotation.

The rate of change of angular velocity over time.

Using standard units for torque (newton-meters), moment of inertia (kilogram-meter squared), and time (seconds).

Net torque equals the moment of inertia multiplied by the angular acceleration.

A diagram showing all forces acting on an object.

The point around which an object rotates (or is assumed to rotate).

The force multiplied by the lever arm (distance from the axis).

Steps to solve rotational dynamics problems (diagram, system, free-body diagram, torques, Newton's 2nd Law, solve, estimate).

Moment of inertia for a thin hoop rotating through its center is MR^2.

Moment of inertia for a solid cylinder rotating through its center is (1/2)MR^2.

Moment of inertia of a rod rotating through its center is (1/12)ML^2.

Moment of inertia for a sphere rotating through its center is (2/5)MR^2.

Energy of rotation calculated as 0.5 x I x ω^2.