Rotational kinetic energy(flywheel) problem

In summary, the task is to design a flywheel that can store the kinetic energy of a 600 kg car traveling at 100 km/hr. The flywheel is to be made of steel and can rotate at a maximum speed of 12,000 rpm. Using the equations for rotational speed, kinetic energy, and moment of inertia, a mass of 0.293 kg and a diameter of 0.1476 m can be calculated for a cylindrical flywheel with a thickness of 50 mm.
  • #1
orangeincup
123
0

Homework Statement


You have been assigned the task of designing a flywheel capable of storing
the translational kinetic energy of a 600 kg car traveling at 100 km/hr. The
flywheel is to be manufactured out of steel and the maximum rotational
speed is 12,000 rpm.
a. Assuming that the flywheel is a uniform cylindrical disk 50 mm in
thickness, calculate the mass and diameter of the flywheel.

Homework Equations


ω=2π/60
TKE=1/2mv^2
Ig=1/2mr^2
RKE=1/2Ig*ω^2

The Attempt at a Solution


Solving for ω[/B]
12000rpm*2pi/60=1256.6 rad/s

Solving for energy TKE
100*1000/3600=27.8m/s
1/2*600*27.8m/s=231481J
Solving for Ig(moment of inertia flywheel)
RKE=1/2Ig*ω^2

231481=1/2Ig*1256.6^2
Ig=0.293KG

At this point I'm not sure how to go further.
 
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  • #2
Can you think of a way to relate the diameter and mass of the wheel using the fact that the wheel is made of steel?
 
  • #3
orangeincup said:

Homework Statement


You have been assigned the task of designing a flywheel capable of storing
the translational kinetic energy of a 600 kg car traveling at 100 km/hr. The
flywheel is to be manufactured out of steel and the maximum rotational
speed is 12,000 rpm.
a. Assuming that the flywheel is a uniform cylindrical disk 50 mm in
thickness, calculate the mass and diameter of the flywheel.

Homework Equations


ω=2π/60
TKE=1/2mv^2
Ig=1/2mr^2
RKE=1/2Ig*ω^2

The Attempt at a Solution


Solving for ω[/B]
12000rpm*2pi/60=1256.6 rad/s

Solving for energy TKE
100*1000/3600=27.8m/s
1/2*600*27.8m/s=231481J
Solving for Ig(moment of inertia flywheel)
RKE=1/2Ig*ω^2

231481=1/2Ig*1256.6^2
Ig=0.293KG

At this point I'm not sure how to go further.
You've made a small mistake in the units for Ig, which should be ...
 
  • #4
TSny said:
Can you think of a way to relate the diameter and mass of the wheel using the fact that the wheel is made of steel?
Density and volume?
So I googled the density of steel is 7830 kg/m^3

So would it be m=d*(h*π*r^2)?

I'm confused on what to do with the Ig value mostly, I know it's not the mass but I don't know how to put it into an equation to solve for mass.
I=mr^2?
I=1/2mr^2?

So if I say 0.293=1/2m*r^2
m=7830*(.05m*π*r^2)

0.293=1/2*7830*(.05m*π*r^2)*r^2

r=0.1476m?
 
  • #5
That looks good. You used the correct expression for I for a cylinder. (As SteamKing pointed out, the unit for I is not kg.)

The density of steel varies, so I'm not sure what value you should use. If you are using a textbook, then you can see if there is a table of densities there that you can use.

Anyway, your answer looks correct to me.
 

1. What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotational motion. It is defined as the energy required to accelerate an object from rest to a given angular velocity.

2. How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is: KE = 1/2 * I * ω^2, where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.

3. What is a flywheel and how does it relate to rotational kinetic energy?

A flywheel is a mechanical device that stores rotational energy. It consists of a heavy disk or wheel that is mounted on an axle and can freely rotate. The kinetic energy of a flywheel is directly related to its rotational speed and moment of inertia.

4. What factors affect the rotational kinetic energy of a flywheel?

The rotational kinetic energy of a flywheel is affected by its mass, size, and angular velocity. The moment of inertia also plays a crucial role in determining the amount of energy stored in a flywheel.

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

Rotational kinetic energy is used in various real-world applications, such as in engines, turbines, and gyroscopes. It is also utilized in energy storage systems, such as flywheel energy storage systems, where the rotational energy is converted back into electrical energy when needed.

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