A revolving slotted arm OA moves a bearing P in a fixed curve shape: r(θ) = Cθ. r = radial distance to O θ = angle the arm OA makes in the x-direction C = known constant Arm OA begins from rest when θ = π/4 and rotates counterclockwise with constant angular acceleration d2θ/dt2 = α. Part 1: Calculate v(t) (the velocity vector) of the P bearing as a function of t. Show result with respect to C, α, and the unit vectors ur (r-direction) and uθ (θ-direction). Part 2: Calculate a(t) (acceleration vector) of the P bearing as a function of t. Show result with respect to C, α, and the unit vectors ur (r-direction) and uθ (θ-direction). Part 3: Calculate magnitude v of the velocity and the magnitude a of the acceleration of P when the angle of the slotted arm is θ = 3π/4.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A revolving slotted arm OA moves a bearing P in a fixed curve shape: r(θ) = Cθ.

r = radial distance to O

θ = angle the arm OA makes in the x-direction

C = known constant

Arm OA begins from rest when θ = π/4 and rotates counterclockwise with constant angular acceleration d2θ/dt2 = α.

Part 1: Calculate v(t) (the velocity vector) of the P bearing as a function of t. Show result with respect to C, α, and the unit vectors ur (r-direction) and uθ (θ-direction).

Part 2: Calculate a(t) (acceleration vector) of the P bearing as a function of t. Show result with respect to C, α, and the unit vectors ur (r-direction) and uθ (θ-direction).

Part 3: Calculate magnitude v of the velocity and the magnitude a of the acceleration of P when the angle of the slotted arm is θ = 3π/4.

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Transcribed Image Text:А P
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