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

Angular acceleration =
`(19\pi^2)/(3)`Ф°

Step-by-step 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*
`(2\pi )/(60)` r° +6 z

Δω= Δ(
`(95\pi )/(3)` r°) +Δ (6z)

as Δr =(ΔФ) Ф° ; Δz=0

Δω=
`(95\pi )/(3)` (ΔФ) Ф°

Δω/Δt =
`(95\pi )/(3)` (ΔФ/Δt)Ф°

as we know ΔФ/Δt is about positive y axis

ΔФ/Δt =6rpm =6*
`(2\pi )/(60)` =
`(\pi )/(5)`

Δω/Δt = (
`(95\pi )/(3)`)(
`(\pi )/(5)`)Ф°

angular acceleration =
`(19\pi^2)/(3)`Ф°