The angular speed of the shaft of a car's engine is 127 rad/s

Question

How many revolutions does it complete in 4.0 hours?

Answer 1

Angular speed ω = 127 rad/sec

Time t = 4 hours

t = 4*60*60 = 14400 sec

2π rad/s = 1 rev/s ⇒ rad/s = (1/2π) rev/s ⇒  1 rad/s = (1/2π) rev/s

ω = 127 rad/sec ⇒ ω = 127(1/2π) rev/s  ⇒ ω = (127/2π) rev/s

Shaft rotates (127/2π) revolutions for 1 sec.

Shaft rotates (127/2π) revolutions for t = 14400 sec is (127/2π)*14400 = 291062.56 ≈ 291063 revolution.

Solution : Shaft of car engine rotates 291063 revolutions in 4 hours.