Answer to Question #7570 in Mechanics | Relativity for brawlf

Question

An electric motor operates at 1800rpm. Find its angular speed in radians/seconds. What is the linear speed of a point 55mm from the axis of rotation? What is its centripetal acceleration?

Answer 1

Angular speed in radians/seconds is:

ω = 1800 r/m = 1800/60 r/s = 300*2π rad/s = 600π rad/s.

The linear speed of a point R=55mm from the axis of rotation is

V = 600π rad/s · R = 600π·55 mm = 33000 mm/s = 330 m/s.

Centripetal acceleration of a point R=55mm from the axis of rotation is

ac = ω²R = (600π)² · 55 = 19800000π mm/s² = 198000π m/s².