Rotational Momentum: Calculating Angular Speed After Cockroach Stops

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SUMMARY

The discussion focuses on calculating the angular speed of a lazy Susan after a cockroach stops running on its rim. The cockroach has a mass of 0.17 kg and runs at a speed of 2.0 m/s on a lazy Susan with a radius of 15 cm and a rotational inertia of 4.9 × 10^−3 kg·m², initially rotating clockwise at 3.9 rad/s. The conservation of angular momentum principle is applied, leading to the equation L_i = L_f, where L_i represents the initial angular momentum and L_f the final angular momentum. The correct calculation of angular speed after the cockroach stops is essential for solving the problem accurately.

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  • Knowledge of the relationship between linear and angular velocity
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Homework Statement


A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm,rotational inertia 4.9 ✕ 10^−3 kg · m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.0 m/s, and the lazy Susan turns clockwise with angular speed ω0 = 3.9 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops.

(a) What is the angular speed of the lazy Susan after the cockroach stops?

Homework Equations


L_i = L_f
L=Iw = mvr

The Attempt at a Solution



L_i = 4.9 ✕ 10^−3 * 3.9 + .17*2.0*.15
L_f = (4.9 ✕ 10^−3)w_f

But when I solve the equations putting L_i = L_f, the w_f I get is wrong. please help!
 
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The cockroach is running counterclockwise and the table is turning clockwise, yet you added theirangular momentum. Is that right?
And what happened to the mass of the cockroach after it stopped on the turntable?
 
oh right.
are my equations right otherwise?
 

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