contestada

A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 31.5 kg. The child grabs and clings to a bar that is 1.25 m from the center of the merry‑go‑round, causing the angular velocity of the merry‑go‑round to abruptly drop from 51.0 rpm to 17.0 rpm . What is the moment of inertia of the merry‑go‑round with respect to its central axis?

Respuesta :

boffeemadrid

Answer:

24.609375 kgm²

Explanation:

I = Moment of inertia of the merry go round

[tex]N_1[/tex] = Initial speed = 51 rpm

[tex]N_2[/tex] = Final speed = 17 rpm

m = Mass of child = 31.5 kg

r = Radius = 1.25 m

In this system the angular momentum is conserved

[tex]IN_1=(I+mr^2)N_2\\\Rightarrow I\times 51=(I+31.5\times 1.25^2)17\\\Rightarrow I\dfrac{51}{17}-I=31.5\times 1.25^2\\\Rightarrow 2I=49.21875\\\Rightarrow I=\dfrac{49.21875}{2}\\\Rightarrow I=24.609375\ kgm^2[/tex]

The moment of inertia of the merry go round is 24.609375 kgm²

Otras preguntas