# Flywheel calculations

## Homework Statement

A flywheel made of glass fibre has been developed by BP to store the kinetic energy of buses when they come to a bus stop. The maximum energy stored in the flywheel is equivalent to the energy lost by a 16,000 kg bus braking from 48 km when it comes to rest. The bulk of the flywheel’s mass is in its rim which moves at 1300 km when the flywheel rotates at the maximum angular velocity of 16,000 rev . After a typical stop of two minutes during which time the flywheel slows down, four fifths of its energy is still available to accelerate the vehicle.

From this data show that the flywheel has the following properties:

1. Maximum kinetic energy = 1.42 MJ (2 marks)

2. Moment of Inertia = 1.01 kg (3 marks)

3. Radius = 0.215 m (2 marks)

4. Minimum mass = 21.9 kg (3 marks)

(Each section must be answered in the order given. You may not assume data from the following sections).

e) Determine also the

5. Determine also the mean frictional torque causing the slowing down in the two minute stop. (6 marks)

## Homework Equations

not really sure!!

## The Attempt at a Solution

I cant figure out how to do this as I don't know how to do it In this order?

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PeroK
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I tried using
and then I didn't know which other equation I could use but I don't know the radius or anything

PeroK
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I tried using View attachment 86949and then I didn't know which other equation I could use but I don't know the radius or anything
Where does the KE come from?

The kinetic energy of an object is the energy it possesses because of its motion?

PeroK
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The kinetic energy of an object is the energy it possesses because of its motion?
Okay, I'll get you started. The energy comes from the bus. It tells you that in the question.

Okay, I'll get you started. The energy comes from the bus. It tells you that in the question.
well yes I understand that part, I just don't understand how I use what ive been given to work it out as im used to using

PeroK
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well yes I understand that part, I just don't understand how I use what ive been given to work it out as im used to using View attachment 86951
How else could you work out the energy of the flywheel? Hint: think about the energy of the bus.

E = ½mv2?

PeroK
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E = ½mv2?
If you mean the energy of the flywheel is equal to the energy of the bus, and you're given the mass and velocity of the bus, then yes!

If you mean the energy of the flywheel is equal to the energy of the bus, and you're given the mass and velocity of the bus, then yes!
yeah that's what I meant, so I use the mass of the bus and the speed from which it is braking from?

PeroK
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yeah that's what I meant, so I use the mass of the bus and the speed from which it is braking from?
Yes, that's what the question implies.

but if I do that I get that E=18432000?

PeroK
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but if I do that I get that E=18432000?
What units are you using? I assume the speed is 48 km/h? What if the speed of the bus was given in mph (miles per hour)? Or cm/s?

What units are you using? I assume the speed is 48 km/h? What if the speed of the bus was given in mph (miles per hour)? Or cm/s?
yes its 48km/h so what I did was (0.5)(16000)(48)^2

PeroK
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yes its 48km/h so what I did was (0.5)(16000)(48)^2
So, why is that wrong? Note that 48 km/h is about 30 mph. So, why not (0.5)(16000)(30)^2?

the answer, Maximum kinetic energy = 1.42 MJ, is given in the question, when 30mph is used you get 7200000 which is also the wrong answer

PeroK
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the answer, Maximum kinetic energy = 1.42 MJ, is given in the question, when 30mph is used you get 7200000 which is also the wrong answer
So, if you take the speed in different units, you get different numerical answers. There is only one set of units in the SI:

Kilograms, Metres, Seconds and Joules

You must use mass in kilograms and speed in metres per second to get KE in Joules.

so how do I change 48km/h into m/s? never mind I got it now!!

Last edited:
PeroK
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so how do I change 48km/h into m/s?
Are you really saying that if a bus is going at 48 km/h, you don't know how far it travels each second?

Are you really saying that if a bus is going at 48 km/h, you don't know how far it travels each second?
ive done it, and done part a, im just getting confused on which equations I need to use for which parts.

so in part b I know I need to use

PeroK
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so in part b I know I need to use View attachment 86958
Yes, you've got the KE now and you're given ##\omega## (although you need to watch the units again), so you should be able to calculate ##I##.

which is ω?

PeroK