# Rotational Momentum: Calculating Angular Speed After Cockroach Stops

• JessicaHelena
In summary, the conversation discusses the scenario of a cockroach running on a rotating lazy Susan and finding a bread crumb. The lazy Susan has a radius of 15 cm and a rotational inertia of 4.9 ✕ 10^−3 kg · m2, and the cockroach has a mass of 0.17 kg and a speed of 2.0 m/s. After the cockroach stops, the angular speed of the lazy Susan is being calculated using the equations L_i = L_f and L=Iw = mvr. However, there is a mistake in adding the angular momentum of the cockroach and the lazy Susan, and the mass of the cockroach is not considered after it stops. Further clarification
JessicaHelena

## 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?

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!

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?

## 1. What is rotational momentum?

Rotational momentum, also known as angular momentum, is a measure of an object's tendency to continue spinning or rotating. It is created by the mass, shape, and speed of an object.

## 2. How is angular speed calculated?

Angular speed is calculated by dividing the change in angle of an object by the time it takes for that change to occur. It is typically measured in radians per second.

## 3. Why is it important to calculate angular speed after a cockroach stops?

Calculating the angular speed after a cockroach stops can help scientists understand the movement and behavior of the cockroach. It can also provide insights into the physical capabilities and limitations of the cockroach.

## 4. What factors can affect the angular speed of a stopped cockroach?

The angular speed of a stopped cockroach can be affected by various factors, including the size and shape of the cockroach, the surface it is moving on, and the force applied to it.

## 5. How can the calculation of angular speed be applied in real life?

The calculation of angular speed can be applied in various real-life situations, such as in the design of machinery and vehicles that involve rotational motion. It can also be used in sports science to analyze the movements of athletes and improve their performance.

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