A riveting machine is driven by a constant-torque 3kW motor. The moving parts including the flywheel are equivalent to 150 kg at 0.6 m radius. One riveting operation takes 1 second and absorbs 10000 N-m of energy. The speed of the flywheel is 300 r.p.m. before riveting. What is the speed (to nearest 10 r.p.m.) after riveting and what is the number of rivets that can be closed per minute?

Concept:

the maximum fluctuation of energy is given by 

Where m is the mass of the flywheel, k is the radius of gyration of the flywheel, ω₁ is the and ω₂ is the maximum and minimum angular velocities of the flywheel. 

Calculation:

Given, P = 3 kW, m = 150 kg, k = 0.6 m

N1 = 450 r.p.m.   or 

Let, ω2 = Angular speed of the flywheel immediately after riveting.

Energy supplied by motor (E2) = 3 kW = 3000 W = 3000 Nm/s

Energy absorbed during one riveting operation (E1) = 10000 Nm/s

the maximum fluctuation of energy,

ΔE = E1 – E2, or Energy to be supplied by the flywheel for each riveting operation per second

ΔE = 10000 – 3000 = 7000 Nm

⇒ ω2 = 26.96 rad / s

Corresponding speed 

E2 = 3 kW = 3000 N-m/sec

But energy absorbed during one riveting operation which takes 1 sec = E1 = 10,000 N-m

Then, number of rivets that can be closed per minute,