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

I = M R^2 /2 = (0.500 kg) (0.06/2 m)^2

I = 2.25 x 10^-4 kg m^2

and w = 60 rad/s

(A) L = I w = 0.0135 kg m^2 / s

(B) Work done = change in KE

W = (2.25 x 10^-4) (60^2 - 0^2) /2

W = 0.405 J  

(C) R' = R [1 + alpha deltaT]

R = 0.03[ 1 + (19 x 10^-6)(100 -20)]

R = (0.03)(1.00152) m

Li = Lf

I w = I' w'

(M R^2 / 2) w = (M R'^2 / 2) w'

w' = (R / R')^2 w

and w' / w = ((R/R')^2)) = 0.997  

  

(d) L' = L

so L' / L = 1

(e) Ke' / KE = I' w'^2 / I w^2

= (R' / R)^2 (w'/w)^2

= (1/0.997)(0.997)^2

= 0.997