Angular Motion and Related Concepts

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• Office hours today: 1:30 to 3:00 pm in Randall 1480.
• If sick, please wear a mask.

Angular Displacement

• Angular displacement is the angular equivalent of linear displacement.
• Measured in radians (2 π rad = 360°; 1 rad ≈ 57.3°).
• Defined as the difference between two angles for the same body.

Angular Quantities

• Average Angular Velocity (ω) = Δθ/Δt.
• Instantaneous Angular Velocity = dθ/dt at a specific point.
• Average Angular Acceleration (α) = Δω/Δt.
• Instantaneous Angular Acceleration = dω/dt.

Angular Quantities as Vectors

• Treated as vectors using the right-hand rule.
• In the x-y plane, angular vectors can only point along ± z axis.
• Rotations defined as clockwise and counterclockwise.

Angular Motion and Acceleration

• For a ladybug on a spinning wheel:
• Angular velocity vector points into the page.
• Angular acceleration vector points out of the page.
• Linear speed (v) is related to angular speed (ω): v = rω.
• Centripetal acceleration: a_rad = rω².
• Tangential acceleration: a_tan = rα.

Moment of Inertia (I)

• Defined as I = Σ(m * r²), where m is mass and r is distance from the rotation axis.
• Moment of inertia indicates how difficult it is to change the rotation of a body.
• Changes based on the mass distribution relative to the axis of rotation.

Kinetic Energy of a Rotating Body

• Total KE = Σ(1/2 * m * (ri * ω)²).
• Depends on the distribution of mass and distance from the axis of rotation.