Question

A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. How many revolutions does the wheel make in attaining the speed of 2000 r.p.m.?

(a) 400

(b) 300

(c) 333.4

(d) 200

The question was asked during an interview.

The origin of the question is Acceleration of a Particle along a Circular Path in section Kinematics & Kinetics of Motion of Machine Kinematics

Answer 1

Right choice is (c) 333.4

For explanation: Solution. Given : N0 = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s

We know that the angular distance moved by the wheel during 2000 r.p.m. (i.e. when ω = 209.5 rad/s),

θ = (ω0 + ω )t/2

  = (0 + 209.5)20/2

  = 2095 rad

Since the angular distance moved by the wheel during one revolution is 2π radians, therefore number of revolutions made by the wheel,

n = θ /2π = 2095/2π = 333.4