107 139
Assignments Done
100%
Successfully Done
In January 2023

# Answer to Question #115565 in Mechanics | Relativity for Jocelyn

Question #115565
A machine part rotates at an angular speed of ωi. Its speed is then increased to ωf at an angular acceleration of α. If both the initial and final angular speeds are now doubled and the angular acceleration remains the same, by what factor is the angular displacement changed?
1
2020-05-14T09:12:23-0400

Given data

Initial angular speed is ωi

Final angular speed is ωf

Angular acceleration is α.

The expression for the angular displacement of machine is

"\\Delta\\theta=\\frac{((\\omega_f)^2-(\\omega_i)^2)}{(2\\alpha)}" .........................(1)

When the both the initial and final angular speeds are now doubled that is ( ω'i =2ωi) and ( ω'f=2ωf), then the new angular displacement is

"\\Delta\\theta '=\\frac{((\\omega'_ f)^2-(\\omega'_i)^2)}{(2\\alpha)}"

"=(\\frac{(2\\omega_f)^2-(2\\omega_i)^2)}{(2\\alpha) } =\\frac{4((\\omega _f)^2-(\\omega_i)^2))}{(2\\alpha)}" ............(2)

From equations (1) and (2), we get

"\\Delta\\theta '=4 \\Delta\\theta"

Hence , the angular displacement is increased by the factor 4.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!