A man stands on a platform that is rotating (without friction) with an angular speed of 1.2 rev/s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man, bricks, and platform about the central vertical axis of the platform is 6.0 k g times m squared. If by moving the bricks the man decreases the rotational inertia of the system to 2.0 k g times m squared, what is the resulting angular speed of the platform in rad/s

Question

Physics

Alexis Roth

Yesterday, 22:38

A man stands on a platform that is rotating (without friction) with an angular speed of 1.2 rev/s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man, bricks, and platform about the central vertical axis of the platform is 6.0 k g times m squared. If by moving the bricks the man decreases the rotational inertia of the system to 2.0 k g times m squared, what is the resulting angular speed of the platform in rad/s

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Karsyn Stewart · Answer 1

resulting angular speed = 3.6 rev/s

Explanation:

We are given;

Initial angular speed; ω_i = 1.2 rev/s

Initial moment of inertia; I_i = 6 kg/m²

Final moment of inertia; I_f = 2 kg/m²

From conservation of angular momentum;

Initial angular momentum = Final angular momentum

Thus;

I_i * ω_i = I_f * ω_f

Making ω_f the subject, we have;

ω_f = (I_i * ω_i) / I_f

Plugging in the relevant values;

ω_f = (6 * 1.2) / 2

ω_f = 3.6 rev/s