# Help: Hamster wheel rotational dynamics

• Ingenue1
In summary, the conversation discusses a scenario where a hamster is running inside a large hollow hamster ball rolling at 5 miles per hour. The hamster weighs .3 kg and the ball has a mass of 1.5 kg and a radius of 0.4m. The questions asked are about the angular velocity of the ball, the change in angular velocity when the hamster does a loop the loop, and the new velocity along the ground in miles per hour. The conversation also brings up the relation between linear velocity and angular velocity, computing moment of inertia for a sphere, and the effect of the loop the loop on the moment of inertia. Finally, the conversation mentions the use of an equation for conservation of angular momentum.
Ingenue1

## Homework Statement

A large hollow hamster ball is rolling along the ground at 5 miles per hour. A hamster is running inside, matching his pace at the bottom of the ball to stay by the ground. The hamster weighs .3 kg, and the ball has a mass of 1.5 kg with a radius of 0.4m.

## Homework Equations

What is the angular velocity of the ball?
The hamster decides to do a loop the loop and grabs the inside of the ball with its claws. What is the new angular velocity of the ball?

What is the new velocity along the ground in miles per hour?

## The Attempt at a Solution

Need at least some attempt at an answer. What relation is there between linear velocity and angular velocity?

How do we compute moment of inertia for a sphere?

What effect does the loop de loop have on the moment of inertia--it is now an additional point mass at radius, 0.4m.

For angular momentum to be conserved, what eqn can we use?

To determine the angular velocity of the ball, we can use the equation ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the radius of the ball. Plugging in the given values, we get ω = (5 mph) / (0.4m) = 12.5 rad/s.

When the hamster grabs the inside of the ball and starts running in a circular motion, the angular velocity of the ball will change. This can be calculated using the conservation of angular momentum, where the initial angular momentum of the system (hamster + ball) is equal to the final angular momentum after the hamster starts running in a circular motion. We can express this as Iω = (I + mR^2) ω', where I is the moment of inertia of the ball, m is the mass of the hamster, R is the radius of the ball, and ω' is the new angular velocity of the ball. Solving for ω', we get ω' = Iω / (I + mR^2). Plugging in the given values, we get ω' = (0.5 kg m^2)(12.5 rad/s) / (0.5 kg m^2 + 0.3 kg)(0.4m)^2) = 8.33 rad/s.

To determine the new velocity of the ball along the ground, we can use the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the ball. Plugging in the new angular velocity of the ball, we get v = (8.33 rad/s) (0.4m) = 3.33 m/s. Converting this to miles per hour, we get v = (3.33 m/s)(2.237) = 7.46 mph.

Therefore, the new angular velocity of the ball is 8.33 rad/s, and the new velocity along the ground is 7.46 mph.

## 1. What is "Help: Hamster wheel rotational dynamics"?

"Help: Hamster wheel rotational dynamics" is a topic that deals with the physics of a hamster wheel in motion. It involves understanding the forces and movements involved in the rotation of a hamster wheel.

## 2. Why is understanding hamster wheel rotational dynamics important?

Understanding hamster wheel rotational dynamics is important for several reasons. Firstly, it allows us to design and improve hamster wheels for the comfort and safety of our furry friends. Additionally, it can also help us understand the principles of rotational motion and apply them to other areas of science and engineering.

## 3. What factors affect the rotational dynamics of a hamster wheel?

The rotational dynamics of a hamster wheel can be affected by various factors such as the size and weight of the hamster, the diameter and material of the wheel, the surface it is placed on, and the friction between the wheel and the surface.

## 4. How does the hamster's motion affect the rotational dynamics of the wheel?

The hamster's motion, specifically its running speed and direction, can greatly affect the rotational dynamics of the wheel. As the hamster runs, it exerts a force on the wheel, causing it to rotate. The direction and speed of the hamster's motion can determine the direction and speed of the wheel's rotation.

## 5. Are there any safety considerations when studying hamster wheel rotational dynamics?

Yes, there are some safety considerations to keep in mind when studying hamster wheel rotational dynamics. It is important to make sure that the hamster wheel is securely attached and stable, and that the hamster is not at risk of falling or getting injured during the experiment. It is also important to handle the hamster with care and to follow ethical guidelines for animal research.

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