Respuesta :
Answer
given,
angular speed of disk = 32 rad/s
mass dropped, m = 1.3 Kg
radius, r = 0.25 m
new rotational velocity = ?
now,
Initial rotational inertia of the disk
[tex]I_1 = \dfrac{1}{2}MR^2[/tex]
Assuming the mass and the radius of the disk is equal to 7.5 Kg and 0.85 m respectively
now,
[tex]I_1 = \dfrac{1}{2}\times 7.5\times 0.85^2[/tex]
[tex]I_1 = 2.71\ Kgm^2[/tex]
Rotational inertia after mass is dropped on it
[tex]I_2 = \dfrac{1}{2}MR^2 + mr^2[/tex]
[tex]I_2 = 2.71 + 1.3\times 0.25^2[/tex]
[tex]I_2 = 2.79\ Kg.m^2[/tex]
using angular momentum conservation
I₁ω₁ = I₂ω₂
2.71 x 32 = 2.79 x ω₂
ω₂ = 31 rad/s
new angular velocity of the disk is ω₂ = 31 rad/s
