The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Angular acceleration of the flywheel?
a) 0.6 rad/s2b) 0.8 rad/s2
c) 0.10 rad/s2
d) none of the above
Explanation: Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m
Angular acceleration of the flywheel
Let α = Angular acceleration of the flywheel.
We know that mass moment of inertia of the flywheel,
I=m.k2 = 2500×12 = 2500 kg-m2
We also know that torque ( T ),
1500 = I .α = 2500 × Î±
or α = 1500 / 2500 = 0.6 rad/s2
The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Kinetic energy of the flywheel after 10 seconds from the start.
a) 50 kJb) 60 kJ
c) 45 kJ
d) none of the above
Explanation: Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m
Angular acceleration of the flywheel
Let α = Angular acceleration of the flywheel.
We know that mass moment of inertia of the flywheel,
I=m.k2 = 2500×12 = 2500 kg-m2
We also know that torque ( T ),
1500 = I .α = 2500 × Î±
or α = 1500 / 2500 = 0.6 rad/s2
Kinetic energy of the flywheel after 10 seconds from start
First of all, let us find the angular speed of the flywheel (ω2) after t = 10 seconds from the start (i.e. ω1 = 0 ).
We know that ω2 = ω1 + α.t = 0 + 0.6 × 10 = 6 rad/s
∴ Kinetic energy of the flywheel,
E = 1/2 I(ω2)2
= 1/2 x 2500 x 62
= 45 000J
= 45 kJ
