Calculating Rotational Inertia: A Puzzling Problem?

In summary, rotational inertia, also known as moment of inertia, is a measure of an object's resistance to rotational motion. It is calculated using the formula I = Σmr², where I is the moment of inertia, m is the mass of each individual particle, and r is the distance of each particle from the axis of rotation. Understanding rotational inertia is important for predicting the behavior of rotating objects and determining the amount of torque needed to change their rotational motion. Factors that affect rotational inertia include mass and distribution of mass around the axis of rotation, with objects having more mass and a greater distance from the axis having a higher rotational inertia. Rotational inertia can be changed by altering the mass or distribution of mass in an object.
  • #1
ViewtifulBeau
50
0
Calculate the rotational inertia of a wheel that has a kinetic energy of 20300 J when rotating at 794 rev/min.
I don't understand this whole rotational inertia thing too well but I thought I found the right equation, but apparently I didn't. I used K = 1/2 * I * w^2
I converted the 794 rev/min to 13.233 rev/s and plugged the numbers into the equation to get 232. The answer is suppose to be in kg*m*m, but withw being in rev/s I don't know what to do.
 
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  • #2
Convert the w to radians per second
 
  • #3


It seems like you are on the right track with using the equation K = 1/2 * I * w^2, which is the correct equation for calculating rotational inertia. However, the unit for rotational inertia is not kg*m*m, but rather kg*m^2. In order to get the correct units, you will need to convert the angular velocity from revolutions per second to radians per second. This can be done by multiplying the revolutions per second by 2π, since there are 2π radians in one revolution. So, your final equation should be K = 1/2 * I * (2πw)^2. Plugging in the values, we get:

20300 J = 1/2 * I * (2π*13.233)^2
20300 J = 1/2 * I * 1752.94
I = (20300 J * 2) / 1752.94
I = 23.13 kg*m^2

So the rotational inertia of the wheel is 23.13 kg*m^2. Hopefully this helps clarify the concept of rotational inertia for you.
 

What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to rotational motion. It depends on both the mass and the distribution of the mass around the axis of rotation.

How is rotational inertia calculated?

The formula for calculating rotational inertia is I = Σmr², where I is the moment of inertia, m is the mass of each individual particle, and r is the distance of each particle from the axis of rotation.

Why is calculating rotational inertia important?

Calculating rotational inertia is important in understanding the behavior of rotating objects. It helps in predicting how an object will respond to external forces and how much torque is required to change its rotational motion.

What factors affect the rotational inertia of an object?

The rotational inertia of an object is affected by its mass and the distribution of that mass around the axis of rotation. Objects with more mass and a larger distance from the axis of rotation have a higher rotational inertia.

Can rotational inertia be changed?

Yes, rotational inertia can be changed by altering the mass or distribution of mass in an object. For example, spreading out the mass further from the axis of rotation will increase the rotational inertia.

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