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A hoop of mass and radius and a solid cylinder of mass and radius are rolling along level ground with the same translational speed. Which object has the greater total kinetic energy?

Respuesta :

Answer:

the kinetic energy of hoop will be more than kinetic energy of solid cylinder

Explanation:

kinetic energy of rolling is given as

[tex]KE = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2[/tex]

here we know that for pure rolling we have

[tex]v = R \omega[/tex]

now we also know that

[tex]I = mk^2[/tex]

here k = radius of gyration

now we have

[tex]KE = \frac{1}{2}mv^2( 1 + \frac{k^2}{R^2})[/tex]

now we know that for

hoop

[tex]\frac{k^2}{R^2} = 1[/tex]

for Solid cylinder

[tex]\frac{k^2}{R^2} = \frac{1}{2}[/tex]

now the kinetic energy of hoop will be more than kinetic energy of solid cylinder

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