# Rotational Dynamics and tangential velocity

• flash
In summary, the problem involves finding the rotational acceleration, final tangential velocity, centripetal acceleration, and angular momentum of a 50.0 g rubber bung that is swung in a horizontal circular path on a 90.0 cm light string with a tension provided by a 250.0 g mass. The centripetal force is given to be 0.25g and the question is asking for the distance and angular velocity at which the force necessary for circular motion is equal to the centripetal force. The formula used is Fc = mrw^2 and as the string gets shorter, the angular velocity for circular motion increases. There is still confusion about the angular acceleration and why the bung would accelerate.
flash

## Homework Statement

Find the rotational acceleration, final tangential velocity and centripetal acceleration of a 50.0 g rubber bung, starting from rest, swung in a horizontal circular path on a very light string of length 90.0 cm. The tension in the string is provided by a mass of 250.0 g. Find the angular momentum of the rubber bung.

I have attached the diagram we were given. This is all the information available.

## The Attempt at a Solution

More looking at a clarification of the question at this stage - as far as I can tell the rubber bung would not accelerate in a circle at all.

#### Attachments

• diagram1.JPG
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What is the centripetal force?

You are, of course, correct that if the object started from rest and the only force on it was the centripetal force, it would not move in a circle, it would move directly toward the center of the circle. However, I note that you quote the problem as saying "swung in a horizontal circular path on a very light string of length 90.0 cm", so it clearly is moving in a circle. At what distance and angular velocity will the force necessary to cause it to move in a circle be the same as the centripetal force?

The centripetal force is 0.25g which must equal mrw^2 right? So if I let m=0.05, r=0.9 and Fc=0.25*9.8 I can solve for omega (23.3). As the string gets shorter (r decreases), the angular velocity necessary for circular motion increases because Fc is constant.
I'm still confused about the angular acceleration. Why would the bung accelerate?

Last edited:

## 1. What is rotational dynamics?

Rotational dynamics is the study of the movement and forces involved in objects that are rotating or spinning. It is a branch of classical mechanics that deals with the motion of rigid bodies.

## 2. How is rotational dynamics different from linear dynamics?

Rotational dynamics differs from linear dynamics in that it takes into account the rotational motion of an object, rather than just its linear motion. This includes factors such as torque, angular velocity, and moment of inertia, which are not considered in linear dynamics.

## 3. What is tangential velocity?

Tangential velocity is the velocity of an object at a specific point on its circular path, tangent to the circle at that point. It is a measure of how fast an object is moving in the direction of its rotation.

## 4. How is tangential velocity related to angular velocity?

Tangential velocity and angular velocity are directly proportional to each other. This means that as the angular velocity of an object increases, so does its tangential velocity at any given point on its circular path.

## 5. What are some real-life examples of rotational dynamics and tangential velocity?

Some common examples of rotational dynamics and tangential velocity include the spinning of a top, the rotation of a Ferris wheel, and the movement of a car's wheels as it turns. These principles are also important in sports such as figure skating and gymnastics, where athletes use rotational motion to perform spins and flips.

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