Question

A uniform brass solid cylinder has a mass, m = 500 g, and a diameter, D = 6 cm and a length L = 1 m. The cylinder rotates about its axis of rotational symmetry at an angular velocity of 60 radians/s on a frictionless bearing.

(a) What is the angular momentum of the cylinder?

(b) How much work was required to increase the angular momentum of the cylinder to this value if the cylinder was initially at rest? Once the cylinder is rotating at 60 radians/s it is heated from 20o C to 100 o C without making mechanical contact to the cylinder.

What is the fractional change in the (c) angular velocity

(d ) angular momentum, and

(e) rotational kinetic energy?

(f ) Explain the results of your calculations in (c) – (e).

Answer 1

a] Moment of Inertia of a solid cylinder is: I = (1/2)MR²

so, angular momentum of the cylinder will be:

b] If initially the cylinder was at rest, then the work done will be:

c]

New Energy = 0.405 + mc[T - T']

E' = 0.405 + (0.5 (920) (80)) = 36800.405 J

moment of inertia remains the same since the mass and the dimension are the same.

the angular momentum will now be:

L = 33.12 kgm²/s [answer - d]

this gives the new rotational frequency of: w = 73600.81 rad/s

e] Rotational kinetic energy will be: