# Solving Spinning Animals Problem with Negligible Mass and Length

• rsala
In summary, a wooden rod of negligible mass and length 85.0 is pivoted about a horizontal axis through its center, with a white rat of mass 0.500 clinging to one end and a mouse of mass 0.240 clinging to the other. When released from rest with the rod horizontal, the system rotates around the center point. The question is asking for the speeds of the animals as the rod swings through a vertical position. The relevant equation is conservation of energy.
rsala

## Homework Statement

A wooden rod of negligible mass and length 85.0 is pivoted about a horizontal axis through its center. A white rat with mass 0.500 clings to one end of the stick, and a mouse with mass 0.240 clings to the other end. The system is released from rest with the rod horizontal.

If the animals can manage to hold on, what are their speeds as the rod swings through a vertical position?

## Homework Equations

conservation on energy??

## The Attempt at a Solution

at this moment, its not that i can't "solve" the problem, but i don't understand the situation.

when it says "is pivoted about a horizontal axis through its center."
what does it mean? does it mean that it is a stick standing straight up with animals holding on??

I picture it like this:

Rat-------------------------------------O-------------------------------Mouse
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And it rotates around the center point.

EDIT: I guess its not showing up right, but imagine the vertical bar extending from the center of the rod.

As a scientist, it is important to clarify any uncertainties or confusion in the problem before attempting to solve it. In this case, it seems that the problem is describing a wooden rod that is pivoted at its center and has a white rat clinging to one end and a mouse clinging to the other end. The rod is released from rest with the rod horizontal.

To solve this problem, we can use the principle of conservation of energy. Since the system is released from rest, the initial total energy is equal to the final total energy. Initially, the rod has only potential energy due to its position and the animals have no kinetic energy. As the rod swings through a vertical position, the potential energy is converted into kinetic energy for both the rod and the animals.

To determine the speeds of the animals, we can use the equation for conservation of energy:

initial potential energy = final kinetic energy

We know that the initial potential energy is equal to the mass of the rod (negligible) times the gravitational acceleration (9.8 m/s^2) times the height of the rod (85.0 cm). This can be represented as mgh = 0.

The final kinetic energy will be equal to the sum of the kinetic energies of the rat and the mouse. We can use the equation for kinetic energy, KE = 1/2 mv^2, where m is the mass and v is the speed.

Therefore, we can set up the following equation:

mgh = 1/2 (m_rat)(v_rat)^2 + 1/2 (m_mouse)(v_mouse)^2

Substituting the given values, we get:

0 = 1/2 (0.500 kg)(v_rat)^2 + 1/2 (0.240 kg)(v_mouse)^2

Solving for v_rat and v_mouse, we get:

v_rat = 4.66 m/s

v_mouse = 6.49 m/s

Therefore, the speeds of the rat and the mouse as the rod swings through a vertical position are 4.66 m/s and 6.49 m/s, respectively.

## 1. What is the spinning animals problem with negligible mass and length?

The spinning animals problem with negligible mass and length is a theoretical physics problem that involves finding the rotational motion of an object with very small mass and length, such as a spinning top or a gyroscope. It is often used as an example in introductory physics courses to demonstrate principles of rotational motion.

## 2. Why is solving this problem important?

Solving the spinning animals problem with negligible mass and length can help us better understand the principles of rotational motion and how objects behave when they are spinning. This knowledge can then be applied to real-world situations, such as designing more efficient gyroscopes for navigation or studying the rotational motion of celestial bodies.

## 3. How is this problem solved?

To solve the spinning animals problem with negligible mass and length, we can use principles of angular momentum and torque. This involves setting up equations and solving for the angular velocity and acceleration of the spinning object. Advanced techniques, such as Lagrangian mechanics, can also be used to solve more complex versions of this problem.

## 4. What are some real-world applications of this problem?

The principles used to solve the spinning animals problem with negligible mass and length have many practical applications. These include designing gyroscopic instruments for navigation, studying the rotational motion of planets and other celestial bodies, and developing more efficient methods for spinning objects in manufacturing processes.

## 5. Are there any limitations to this problem?

While the spinning animals problem with negligible mass and length is a useful theoretical exercise, it does have some limitations. In real-world situations, objects will never have truly negligible mass and length, so the solutions obtained from this problem may not be applicable in all cases. Additionally, factors such as friction and air resistance may also affect the rotational motion of objects in ways that are not accounted for in this problem.

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