Moment of Inertia and Torque Concepts

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

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13 Terms

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Moment of Inertia

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

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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.

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Conservation of Energy

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

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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.

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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.

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Lever Arm

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

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Angular Velocity (ω)

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

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Angular Acceleration (α)

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

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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).

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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.

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Solid Sphere Moment of Inertia

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

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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.

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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.