angular velocity

Question

2.3 The wheel of a locomotive has a diameter of 450 mm, and the locomotive is travelling at 90 km/h. Calculate the angular velocity of the wheel.

Answer 1

2.3)

The "angular velocity" is the number of times the wheel revolves in some named time period. So this question is asking me to find the number of times the wheel twirls around in one minute.

Locomotive diameter d = 450 mm

Substitute : 1 mm = (10^-3) m

d = 450 × 10^-3 m

Locomotive traveling speed v = 90 km/h

We need to convert km/h into meter/minute.( 1 km/h = (10³/60 ) mm/minute

v = 90 (10³/60 ) m/min

v = 1500 m/min

The number of circumferences which fit inside the total distance is the number of times the wheel revolves( angular velocity ) in that time period.

Angular velocity ω = (speed)/(circumference of wheel) = v/πd

ω = (1500)/(450(10^-3)π)

   = 3333.33/π

   = 1061.57 rpm

ω = 1062 rpm

(rpm = revolutions per minute)

The solution is 1062 revolutions of locomotive wheel per minute