Moment of Inertia and Torque Concepts

Flashcards covering key vocabulary and concepts related to moment of inertia and torque, providing definitions and important relationships.

Moment of Inertia

A quantity that characterizes the rotational inertia of a body, depending on the rotation axis.

Kinetic Energy (KE) in Rotation

The energy of a body rotating around a fixed axis, expressed as KE = 1/2 I ω², where I is moment of inertia and ω is angular velocity.

Conservation of Energy

The principle stating that the total energy (GPE + KE) in an isolated system remains constant.

Parallel-Axis Theorem

A theorem that states the moment of inertia about any axis parallel to and a distance d away from the center of mass axis is I = I_Cm + Md².

Torque (τ)

The measure of the turning force on an object, defined as τ = r × F, where r is the distance from the pivot point to the point where the force is applied.

Lever Arm

The shortest distance from the axis of rotation to the line of action of the force.

Angular Velocity (ω)

The rate of change of angular position of a rotating object, typically measured in radians per second.

Angular Acceleration (α)

The rate of change of angular velocity, usually measured in radians per second squared.

Translational vs. Rotational Dynamics

Translational dynamics deals with linear motion quantities (distance, velocity, acceleration) while rotational dynamics involves angular quantities (s, v, a replaced by θ, ω, α).

Thin-walled Hollow Cylinder Moment of Inertia

The moment of inertia of a thin-walled hollow cylinder is I = M R², where M is mass and R is the radius.

Solid Sphere Moment of Inertia

The moment of inertia of a solid sphere is I = 2/5 MR².

Hollow Cylinder Moment of Inertia

The moment of inertia for a hollow cylinder is I = 1/2 M(R₁² + R₂²), where R₁ and R₂ are the inner and outer radii.

Magnitude of Torque

Given by τ = r F sin φ, where r is the distance to the axis, F is the force, and φ is the angle between the force vector and the lever arm.