Respuesta :
Answer:
w = 2 rad / s counterclockwise
Explanation:
This is an exercise in angular momentum, we define a system formed by the two wheels in such a way that the torques during contact have been internal and the angular moeoto0o is conserved
L₀ = L_f
We assume that the counterclockwise rotations are positive, let's look for the initial moment before the collision
L₀ = I w₁ + I w₂
where the angular velocity of the first wheel is w₁ = - 2.00 rad / s and the angular velocity of the second wheel is w₂ = 6.0 rad / s
As the wheels collide and remain in unity, the final angular momentum after the collision
I_total = 2 I
L_f = I_total w
we substitute
I w₁ + I w₂ = I_total w
w = [tex]\frac{I w_1 + Iw_2}{I_{total} }[/tex]
w = [tex]\frac{I \ (w_1+w_2)}{2 \ I}[/tex]
w = [tex]\frac{w_1 +w_2}{2}[/tex]
let's calculate
w = [tex]\frac{-2.0 + 6.0}{2}[/tex]
w = 2 rad / s
the positive sign indicates that the rotation is counterclockwise
The final angular velocity will be 2 rad /s counterclockwise. The pace of transition of angular displacement is described as angular velocity.
What is angular velocity?
The rate of change of angular displacement is defined as angular velocity and it is stated as follows:
ω = θ t
The given data in the problem is;
[tex]\omega_1[/tex] is the angular velocity of wheel 1= 2.0 rad/s
[tex]\omega_2[/tex] is the angular velocity of wheel 2= 6.0 rad/s
[tex]\rm \omega_f[/tex] is the final angular velocity=?
As the wheel collides the initial momentum is equal to the final momentum;
Momentum before collision
[tex]\rm L_0 = I \omega_1 + I \omega_2[/tex]
Momentum after the collision when the two-wheel becomes one wheel;
[tex]\rm \I_ {total }= 2 I \\\\ L_f= I_{total}\omega \\\\[/tex]
From the conservation of momentum principle;
[tex]\rm L_i = L_f \\\\ I \omega_1 + I \omega_2 = I_{total}\omega \\\\ \rm \omega= \frac{ I \omega_1 + I \omega_2 }{2I} \\\\ \omega = \frac{\omega_1 + \omega_2}{2} \\\\[/tex]
[tex]\omega=\frac{-2.0+ 6.0}{2} \\\\ \omega=2\ rad/sec[/tex]
Hence the final angular velocity will be 2 rad /s counterclockwise.
To learn more about the angular velocity refer to the link;
https://brainly.com/question/1980605
