Final angular velocity of dropped yoyo

AI Thread Summary
The discussion centers around calculating the final angular velocity of a yo-yo dropped from a height with an initial velocity. The user initially struggled with the conservation of energy approach, leading to an incorrect answer. Key points included the importance of including initial rotational kinetic energy and correctly applying the moment of inertia formula for the yo-yo. After correcting their calculations and understanding the need to treat the yo-yo as a whole rather than as separate disks, the user successfully arrived at the correct final angular velocity of 610 rad/s. This highlights the significance of careful application of physics principles in problem-solving.
clementc
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Homework Statement


Hey guys,
I just read Physics, by Halliday, Resnick and Krane. There's a chapter on rotational dynamics, and the example goes like this:
A yo-yo of total mass M = 0.24kg consists of two disks of radius R = 2.8cm connected by a thin shaft of radius R0 = 0.25cm. A string of length L = 1.2m is wrapped around the shaft. If the yo-yo is thrown downward with an initial velocity of v0 = 1.4m/s, what is its rotational velocity when it reaches the end of the string?

Homework Equations


KE = \frac{1}{2} mv^2
Rotational KE = \frac{1}{2} I{\omega}^2
I of a cylinder = \frac{1}{2} mr^2
Conservation of energy

The Attempt at a Solution


The way the book did it was really strange and long, so I tried doing it using conservation of energy, but got the wrong answer. Can anyone see what's wrong here?
[PLAIN]http://img151.imageshack.us/img151/6251/rotational.png
Their answer was 610 rad/s, but I really don't know where I went wrong here. Any help would be very greatly appreciated. Thanks!
 
Last edited by a moderator:
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You forgot to add the initial rotational energy when you summed up for the initial kinetic energy.

The rotational inertia of the disk(s) is I = (1/2)MR2, and the rotational energy is KEr = (1/2) I ω2. So there's two factors of 1/2 in there.
 
Oh oops yeah forgot about the initial rotational KE
And sorry my working was a bit unclear - i actually multiplied across all terms by 2 so one of those factors of 1/2 disappeared

This is my new working, but its still giving me a different answer of 433 rad/s =(
Sorry about this, but could you please please look through this new working? i really can't find anything wrong with it but the answers 610 rad/s
Thank you very very much. its just been nagging me all day and i have a really really big exam coming up on saturday. thanks a lot

[PLAIN]http://img851.imageshack.us/img851/3142/rotation2.png
 
Last edited by a moderator:
You're still missing a (1/2) on the rotational energy term on the RHS. This is before you multiplied through by 2.
 
OH OF COURSE! thank you so so much sir =DD thank you thank you thank you!
im such an idiot ==; i treated the two disc separately at first and forgot that the mass in 1/2mr^2 was the mass of the entire yoyo.
the answer did indeed come out to 610 rad/s =) thanks so much!
 

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