Question

. A sphere of mass 25 kg and diameter 0.4 m is revolving about its geometrical axis at the rate of 2100 revolutions per min. Calculate its : (i) moment of inertia, (ii) angular momentum. Ans. (i) 0.4 kg-m”, (ii) 88 kg-m²/s.​

Answer 1

Explanation:

Refer to the above attachment.

Answer 2

Given:

A sphere of mass 25 kg and diameter 0.4 m is revolving about its geometrical axis at the rate of 2100 revolutions per min.

To find:

• Moment of inertia
• Angular momentum

Calculation:

First, let's convert angular velocity from RPM (revolutions per minute) to rad/s:

• 2100 RPM = 2100 × 2π/60 = 70π rad/sec.

Now, moment of inertia of the sphere will be:

MI = ⅖ × m × r²

=> MI = ⅖ × 25 × (0.2)²

=> MI = 10 × 0.04

=> MI = 0.4 kg m².

Now, angular momentum will be :

L = I × w

=> L = 0.4 × 70π

=> L = 87.96

=> L $\approx$ 88 kg m²/sec.

Hope It Helps.