A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is a 3 R 2 ω . T

Question

A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is a 3 R 2 ω . The value of a will be

TestHub · Accepted Answer

Angular momentum of a rotating and translating body is given by,

$L_{O} = m v R + I ω = m v R + \frac{2}{3} M R^{2} ω$

For rolling, $v = ω R$

$\Rightarrow L_{O} = m ω R^{2} (1 + \frac{2}{3}) = \frac{5}{3} m ω R^{2}$

Therefore, the value of $a = 5$ .

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