Respuesta :
Answer:
0.26087 rad/s
Explanation:
mass of the child (m) = 40 kg
velocity (v) = 3 m/s
distance (r) = 1.5 m
moment of inertia (I) = 600 kg.m^{2}
rotational momentum of the child = Iω
where
- moment of inertia of the child (I) = [tex]mr^{2}[/tex] = 40 x 1.5 x 1.5 = 90 kg/m^{2}
- angular velocity (ω) = velocity / distance = 3 / 1.5 = 2 rad/s
rotational momentum of the child = Iω = 90 x 2 = 180 kg[tex]m^{2}[/tex]/s
from the conservation of momentum the initial momentum of the child must be the same as the final momentum of the child
initial momentum of the child = final momentum of the child
180 = (90 + 600) ω
180 = 690 ω
ω = 180 / 690 = 0.26087 rad/s
The angular or rotational momentum is the conserved quantity that has both magnitude and direction. It is given by:
[tex]\rm L = mvr[/tex]
Where,
L = rotational/angular momentum, m = mass, v = velocity and r = radius
The angular speed will be 0.26087 rad/s.
The speed can be estimated as:
Given,
- Mass of the child (m) = 40 kg
- Velocity (v) = [tex]3 \rm \;m/s[/tex]
- Distance (r) = 1.5 m
- Moment of inertia (I) = [tex]600 \;\rm kgm^{2}[/tex]
Rotational momentum is calculated by Iω.
Where,
- Moment of inertia of the child (I) = [tex]\rm mr^{2}[/tex]
[tex]\begin{aligned}&= 40 \times (1.5)^{2} \\&= 90 \rm kg/m^{2}\end{aligned}[/tex]
- Angular velocity (ω) = [tex]\rm \dfrac{velocity}{distance}[/tex]
[tex]\begin{aligned}&= \dfrac{3 }{1.5} \\&= 2 \rm rad/s\end{aligned}[/tex]
Rotational momentum of the child = Iω
[tex]\begin{aligned} \rm I\omega &= 90 \times 2 \\\\&= 180 \;\rm kgm^{2}/s\end{aligned}[/tex]
The final and the initial momentum would be the same according to the conservation law.
Initial momentum = Final momentum
180 = (90 + 600) ω
180 = 690 ω
Solving further:
[tex]\begin{aligned}\omega &= \dfrac{180}{690}\\\\&= 0.26087 \;\rm rad/s\end{aligned}[/tex]
Therefore, 0.26087 rad/s is the angular speed.
To learn more about momentum follow the link:
https://brainly.com/question/904448
