A solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of ωi. The sphere is s

Question

1 month ago

7

A solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of ωi. The sphere is s

lowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness D 2 . By what factor is the angular velocity changed? (Give your answer as a factor of ωi.)

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-03-01T06:13:34+03:00

ValentinkaMS [3.4K]1 month ago

5 0

Answer:

0.6

Explanation:

The formula for the volume of a sphere is $\frac{4}{3} \pi (\frac{D}{2})^3$

Thus $\pi * r^2 * (\frac{D}{2} ) = \frac{4}{3} \pi (\frac{D}{2})^3$

The radius of the disk is $1.15(\frac{ D}{2} )$

Applying angular momentum conservation;

The $M_i$ of the sphere = $\frac{2}{5} m \frac{D}{2}^2$

$M_i$ of the disk = $m*\frac{ \frac{1.15*D}{2}^2 }{2}$

$\frac{wd}{ws} = \frac{\frac{2}{5}m * \frac{D}{2}^2}{ m * \frac{(\frac{`.`5*D}{2})^2 }{2} }$

= 0.6