Question

The rotor of an electric motor rotates at the constant rate ω1 =1900 rpm. Determine the angular acceleration of the rotor as the motor is rotated about the y axis with a constant angular velocity ω2 of 6 rpm counterclockwise when viewed from the positive y axis.

Answer 1

Answer:

Angular acceleration =$\frac{19\pi^2}{3}$Ф°

Explanation:

• Angular acceleration is rate of change of angular velocity vector

Here angular velocity is combination of two types of rotation

Using cylindrical coordinates( r°=radial unit vector;Ф°=angular unit vector)

ω=1900*$\frac{2\pi }{60}$  r° +6 z

Δω= Δ($\frac{95\pi }{3}$  r°) +Δ (6z)

as Δr =(ΔФ) Ф°  ; Δz=0

Δω=$\frac{95\pi }{3}$   (ΔФ) Ф°

Δω/Δt = $\frac{95\pi }{3}$  (ΔФ/Δt)Ф°

as we know ΔФ/Δt is about positive y axis

ΔФ/Δt =6rpm =6* $\frac{2\pi }{60}$ =$\frac{\pi }{5}$

Δω/Δt = ($\frac{95\pi }{3}$)($\frac{\pi }{5}$)Ф°

angular acceleration =$\frac{19\pi^2}{3}$Ф°