# Solving for Rotational Velocity of a Ring and Bug System | Homework Question

• aigerimzh
In summary, the conversation discusses a problem involving a ring of mass M and radius R on a frictionless table, with a bug of mass m walking around it at a constant speed v. The problem asks for the rotational velocity of the ring at two different points. The attempt at a solution involves using equations for momentum and angular momentum, but the answer does not match the one given in the book. The conversation also includes a question about the meaning of the ring being pivoted to the table at its rim.
aigerimzh
1. Homework Statement

A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug (a) is halfway around and (b) back at the pivot?

2. Homework Equations

p=mv

3. The Attempt at a Solution

If I assume that only momentum and angular momentum are conserved, and that the bug still has speed v with respect to the ring, I get these equations:

-mv = m(v + V) + Mv
-mRv = -mR(v + V) + M(R^2)(omega)

where V is the velocity of the ring and omega is the angular velocity. I solve these equations for omega, and I don't get the answer in the book.

Where did I go wrong? Thanks in advance for all your help.

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"It is pivoted to the table at its rim."

What does this mean?

LawrenceC said:
"It is pivoted to the table at its rim."

What does this mean?

It is in attached picture

## 1. What is the relationship between ring size and mass?

The relationship between ring size and mass depends on the material of the ring. For example, a ring made of gold will have a different mass than a ring made of silver, even if they are the same size. The density of the material also affects the mass of the ring.

## 2. How does the shape of a ring affect its mass?

The shape of a ring can greatly affect its mass. A thicker or wider ring will generally have a higher mass than a thinner or narrower ring, even if they are made of the same material. This is because more material is used to create the larger ring, resulting in a higher mass.

## 3. Can the mass of a ring change over time?

Yes, the mass of a ring can change over time due to various factors such as wear and tear, corrosion, and accumulation of dirt or other substances. The amount of change in mass will depend on the material of the ring and its exposure to these factors.

## 4. How can the mass of a ring be measured?

The mass of a ring can be measured using a scale or balance. Jewelers often use a precision balance to measure the mass of rings accurately. It is also possible to estimate the mass of a ring by using its dimensions and the density of the material it is made of.

## 5. Does the mass of a ring affect its durability?

Generally, the mass of a ring does not directly affect its durability. However, a heavier ring may put more pressure on the wearer's finger, potentially causing discomfort or even injury. The durability of a ring depends more on the quality of the material and its design rather than its mass.

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