Physics, 26.03.2021 02:40 ezequielromero41

Two wheels with identical moments of inertia are rotating about the same axle. The first is rotating clockwise at 2.0 rad/s, and the second is rotating counterclockwise at 6.0 rad/s. If the two wheels are brought into contact so that they rotate together, their final angular velocity will be

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Answer from: squawk1738

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 = $\frac{I w_1 + Iw_2}{I_{total} }$

w = $\frac{I \ (w_1+w_2)}{2 \ I}$

w = $\frac{w_1 +w_2}{2}$

let's calculate

w = $\frac{-2.0 + 6.0}{2}$

w = 2 rad / s

the positive sign indicates that the rotation is counterclockwise

Answer from: Quest

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Answer from: Quest

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