Work and Rotational Kinetic Energy

In summary, work in the context of rotational kinetic energy refers to the energy transferred to or from an object due to a force causing it to rotate. It is different from linear kinetic energy, which is the energy of an object's linear motion. The rotational kinetic energy of an object is affected by its moment of inertia, angular velocity, and angular acceleration. Work done on an object can be negative in this context, and rotational kinetic energy is used in various real-life applications, such as in machinery, sports, and vehicle design.
  • #1
G-reg
44
0

Homework Statement


A 38.0 kg wheel, essentially a thin hoop with radius 1.13 m, is rotating at 280 rev/min. It must be brought to a stop in 15.0 s.
(a) How much work must be done to stop it?

Homework Equations


change in KE = (1/2)Iwi^2 - (1/2)Iwf^2
I = (1/2)mr^2

The Attempt at a Solution


(1/2)[(1/2)(38)(1.13)^2](28pi/3) = 355.686 kg(m)^2/s

I don't see where the time comes into play though..can anyone help?
 
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  • #2
(1/2)[(1/2)(38)(1.13)^2](28pi/3)
It should be
(1/2)[(1/2)(38)(1.13)^2](28pi/3)^2

To find the work done, time is not necessary.
 
  • #3
Oh ok, I get it now!
Thank you so much!
 

Related to Work and Rotational Kinetic Energy

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

In the context of rotational kinetic energy, work is the amount of energy transferred to or from an object due to a force acting on it and causing it to rotate. It is measured in joules (J).

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

Rotational kinetic energy is the energy an object possesses due to its rotation, while linear kinetic energy is the energy an object possesses due to its linear motion. They are both forms of kinetic energy, but they have different formulas for calculation and are measured in different units.

3. What factors affect the rotational kinetic energy of an object?

The rotational kinetic energy of an object is affected by its moment of inertia (a measure of how difficult it is to change its rotation), angular velocity (how fast it is rotating), and angular acceleration (how quickly its rotation is changing).

4. Can the work done on an object be negative in the context of rotational kinetic energy?

Yes, the work done on an object in the context of rotational kinetic energy can be negative. This occurs when the force acting on the object is in the opposite direction of its rotation, resulting in a decrease in its rotational kinetic energy.

5. How is rotational kinetic energy used in real-life applications?

Rotational kinetic energy is used in many real-life applications, such as in the operation of motors, turbines, and other machinery. It is also important in sports, such as in the spinning of a ball in sports like baseball and bowling. Additionally, the concept of rotational kinetic energy is used in the design and optimization of vehicles and other mechanical systems.

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