# Homework Help: Find watts from rotational kinetic energy

1. Apr 12, 2013

### Sneakatone

a)I used the equation KE=1/2Iw^2

I=mR^2 ---> 1.5x10^30*20000^2
w=2.1*2pi
KE=1/2(1.5x10^30*20000^2)(2.1*2pi)^2=5.2x10^40 J
t=2.1 rev/s / 1.4x10^-15 rev/s^2=1.5x10^15 seconds

5.2x10^40 J/1.5*10^15 seconds =3.4x10^25 watts

B)1.15*10^15 s=1.1*10^18 years

I feel like this method is correct.

2. Apr 12, 2013

### Sneakatone

edit

a)I used the equation KE=1/2Iw^2

I=mR^2 ---> 1.5x10^30*20000^2
w=2.1*2pi
KE=1/2(1.5x10^30*20000^2)(2.1*2pi)^2=5.2x10^40 J
t=2.1 rev/s / 1.4x10^-15 rev/s^2=1.5x10^15 seconds

5.2x10^40 J/1.5*10^15 seconds =3.4x10^25 watts

B)1.15*10^15 s=1.1*10^18 years

I feel like this method is correct.

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3. Apr 12, 2013

### Dick

There some problems there. For one thing the moment of inertia of a sphere is (2/5)MR^2. For another you are supposed to assume the rate of energy loss is constant, not that the rate of angular deceleration is constant. Finally saying "1.15*10^15 s=1.1*10^18 years" is just plain silly. A year is much longer than a second.

4. Apr 12, 2013

### Sneakatone

using the inertia equation I have 2.4x10^38.
making KE=2*10^40

5. Apr 12, 2013

### Dick

I don't think you are rounding correctly for the first answer if you want two significant figures. And you didn't pay any attention to my second comment. The rate of deceleration isn't a constant. The rate of energy loss is. You can't divide the energy by the expected lifetime given constant deceleration. Differentiate the KE expression to get dKE/dt in terms of dw/dt.

6. Apr 12, 2013

### Sneakatone

the derivative would be Iw

7. Apr 12, 2013

### Dick

No, that's the derivative with respect to w. You want the derivative with respect to t. Use the chain rule.

8. Apr 12, 2013

### Sneakatone

I got (w^2)/2

9. Apr 12, 2013

### Dick

How? KE=(1/2)*I*w^2. Take d/dt of both sides. I is constant. w isn't. It's a function of t.

10. Apr 12, 2013

### Sneakatone

would it be just w?

11. Apr 12, 2013

### Dick

No!, why would you think that? You're just guessing. Use the chain rule!
dKE/dt=d((1/2)*I*w^2)/dw*dw/dt.

12. Apr 12, 2013

### Sneakatone

derivative of the outside 1/2Iw^2=Iw
derivative of the inside Iw=I

so final derivative = I^2W

13. Apr 12, 2013

### Dick

The derivative with respect to w is Iw, that's the outside. You've got that. Now the 'inside' is just w. You want to differentiate that with respect to t. What is it?

You should really review the chain rule.

14. Apr 12, 2013

### Sneakatone

would this involve a derivative being differentiating something with a y leaving y' on one side?
if so it would be 2Iw

15. Apr 12, 2013

### Dick

I'll give you a closely related example. If F=Ky^3, then dF/dt=K*3*y^2*dy/dt. The K*3*y^2 is the derivative of the 'outside', the dy/dt is the derivative of the 'inside'.

Like I said you are really thrashing around on this. Review it. For now can you apply that pattern to this problem?

16. Apr 12, 2013

### Sneakatone

dKE/dt=Iw*dw/dt

17. Apr 12, 2013

### Dick

Right. Once more review this. Now use that to find watts.

18. Apr 12, 2013

### Sneakatone

what am I suppose to plug in for dw/dt?

19. Apr 12, 2013

### Dick

What they gave you in the problem statement.

20. Apr 12, 2013

### Sneakatone

can dw/dt also be power=F*v?
I dont know it it is given or if I should solve for it.

21. Apr 12, 2013

### Dick

dw/dt is the rate at which w is changing. If you read the problem statement, they GAVE you that. Read it again. Please?

22. Apr 12, 2013

### Sneakatone

(6*10^38)*(13.19)*(1.4*10^-15)=1.1*10^25 watts

23. Apr 12, 2013

### Dick

I is wrong, I'm not sure why but it looks like you just used MR^2. w is ok. Yay! dw/dt is wrong. I do know why for that one. You forgot the 2*pi. Could you please sit down and try to work this out carefully??

24. Apr 12, 2013

### Sneakatone

(2.4x10^38)(13.19)(1.4*10^-15*2pi)=2.78*10^25 watts