A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre

<p>By the principle of conservation of angular momentum, the total angular momentum of the system &#40;platform + person&#41; remains constant.<br>L_initial = L_final<br>I_initial * ω_initial = I_final * ω_final<br>Initial state: Person is on the rim.<br>I_initial = I_platform + I_person_rim = (1/2)M_platform R² + M_person R²<br>Final state: Person is at the center.<br>I_final = I_platform + I_person_center = (1/2)M_platform R² + 0<br> [ (1/2) (200)R² + (80)R²] * 5 rpm = [ (1/2) (200)R²] * ω_final<br> (100R² + 80R²) * 5 = (100R²) * ω_final<br>180R² * 5 = 100R² * ω_final<br>ω_final = (180 * 5) / 100 = 9 rpm.</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment