Question

A homogenous solid sphere has a mass of 20 kg. Its radius of
gyration about a diameter is 10 cm. Find its moment of inertia and
angular momentum rotating at 120 rpm

Answer 1

Given info : A homogeneous solid sphere has a mass of 20 kg. its radius of gyration about diameter is 10cm.

To find : its moment of inertia and angular momentum rotating at 120 rpm are ..

solution : moment of inertia about an diameter of sphere is given by, I = 2/5 MR²

so radius of gyration, k = √(2/5) R

⇒10/100 m = √(2/5) R

⇒1/100 = 2/5 R²

⇒R² = 1/40

⇒R = 1/√40 m

now moment of inertia , I = Mk²

= 20kg × (10/100 m)²

= 20 × 1/100 kgm²

= 0.20 kgm²

angular velocity, ω = 120 rpm = 120 × 2π/60 rad/s

= 4π rad/s

angular momentum = Iω

= 0.20 kgm² × 4 × 3.14 rad/s

= 2.512 kgm²/s

Therefore the moment of inertia and angular momentum of sphere are 0.2 kgm² and 2.512 kgm²/s respectively.