# Work and rotational Kinetic Energy

• frig0018
In summary, the problem involves a 32.0 kg wheel with a radius of 1.20 m, rotating at 280 rev/min. To bring it to a stop in 15.0 s, the angular acceleration must be determined. The formula for work as a change in kinetic energy can be used to solve for the amount of work needed.

## Homework Statement

A 32.0 kg wheel, essentially a thin hoop with r=1.20 m is rotating at 280 rev/min. It must be brought to stop in 15.0 s. How much work must be done to stop it?

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## The Attempt at a Solution

I=mr^2=46.08 kg*m^2
W=(1/2)I$$\omega$$f^2 - (1/2)I$$\omega$$i^2
W=$$\tau$$($$\Delta$$$$\theta$$)
$$\tau$$=I$$\alpha$$
Rev in 15 sec = 70 rev => 140$$\Pi$$ radians in 15 sec.

I'm not sure which equation(s) to use. I've tried plugging numbers into all of them and getting stuck or wrong answers. Thanks!

Remember, work is a change in kinetic energy. Do you know the formula for kinetic energy of a rotating object?

i thought it was
W = delta K = 1/2(I)(omega final)^2 - 1/2(I)(omega initial)^2...?
or do i use the formula
W= (integral from theta initial to theta final) torque d-theta?

… one step at a time …

frig0018 said:
A 32.0 kg wheel, essentially a thin hoop with r=1.20 m is rotating at 280 rev/min. It must be brought to stop in 15.0 s. How much work must be done to stop it?

Hi frig0018!

First step: what angular acceleration is needed to stop it in 15 s?

## 1. What is work in the context of rotational kinetic energy?

Work is the force applied to an object multiplied by the distance over which the force is applied. In rotational kinetic energy, work is the force applied to an object that is rotating about an axis, multiplied by the distance from the axis to the point where the force is applied.

## 2. How is rotational kinetic energy different from linear kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation about an axis, while linear kinetic energy is the energy an object possesses due to its motion in a straight line. The main difference between the two is the axis of rotation, as rotational kinetic energy depends on the distance from the axis to the point where the force is applied, while linear kinetic energy depends on the speed and mass of the object.

## 3. What is the formula for calculating rotational kinetic energy?

The formula for rotational kinetic energy is ½ Iω², where I is the moment of inertia and ω is the angular velocity. The moment of inertia is a measure of an object's resistance to changes in its rotation, and the angular velocity is the rate at which an object is rotating.

## 4. How does rotational kinetic energy affect an object's stability?

Rotational kinetic energy can affect an object's stability by influencing its center of mass. If an object has a high rotational kinetic energy, it will have a larger moment of inertia and a higher center of mass, making it less stable. On the other hand, a lower rotational kinetic energy will result in a smaller moment of inertia and a lower center of mass, making the object more stable.

## 5. What are some real-life applications of rotational kinetic energy?

Rotational kinetic energy is involved in many everyday activities, such as throwing a ball, riding a bike, and driving a car. In engineering, it is important in designing and analyzing rotating machinery, such as turbines and engines. It is also crucial in understanding the movement and stability of objects in sports, such as gymnastics and figure skating.