I used this formula, I found the number of frames using loggerpro from the start of when it left my hand to the bottom of the string. Here is a google doc link with the formula I derived https://docs.google.com/document/d/1CUXdOLSOxUnFp5koqwsUnWmu8TxhrVlvJn2r7XnVTcg/edit?usp=sharing
I skimmed through much of this thread but I would agree a final result of ~340 m/s^2 is quite a bit bigger than expected, especially when compared to say a pro baseball pitch of 98m/s^2.
I think its important to understand where the acceleration of the yoyo comes from! The yoyo accelerates due to the torque applied on it from the string being pulled out of the yoyo (or the yoyo being pulled from the string depending on how you view it!) Gravity and the force from your hand also help it along depending on how you throw.
I think the one issue is that the yoyo does not accelerate over the exact length of the string like @zhuangyuhao said. The path of the yoyo is not a well defined shape as the yoyo moves on a curve that depends on the length of the string at that point of the throw.
I think it is also important to better define what we are looking for. Acceleration is defined as Acceleration=Force/Mass. The yoyo does not accelerate linearly (doesnât just move in a straight line from point A to B) it accelerates in multiple directions over the entire throw (this also includes rotational acceleration). The approximations (a=2d/t^2, where t=droptime and d=stringlength) you make to find the linear acceleration make sense to me and I think the only likely issue is the timing. With something so quick it is hard to measure the time precisely, when the whole event is .05 sec even 1/100 sec is significant!
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Reading through responses I feel like thereâs some confusion about what weâre talking about. I think everyone has been correct in their inputs so far but it seems like weâre not sure if weâre talking about linear acceleration (up-down) or if weâre talking about rotational acceleration (centripetal). Iâm seeing good stuff for both of these in responses but theyâre not at all the same thingâ@Adam1 maybe you can provide some clarification?
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In the original formula, you should have initial velocity, no? Because the yoyo already has velocity due to the motion of the arm and hand during the throwing motion, before the yo-yo leaves the hand.
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I will try to help shortlyâŚ
I am going to go sit under a tree outside and wait for a falling Apple to hit me on the head.
If the Apple knocks enough dust off my brain, Iâll be back with more useful information.
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@Adam1 I found the error.
d is incorrect. It is not the length of the string.
d is the distance of your throwing motion. It is the distance the yoyo moves from when you begin your throw to when it leaves your hand.
If you are measuring the acceleration before the yoyo leaves the hand, vi = 0 and d must be the length of your throwing motion.
If you are measuring the acceleration of the yoyo after it leaves the hand, vi does not equal 0. vi is the speed of the yoyo just as it leaves your hand and d is the length of the string.
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Ack! Actually thinking it over, what I said in my last two posts is correct however it still wouldnât account for the massive numbers you are seeing for acceleration. I think there is an issue with your time measurements.
Can you give us more info on how you are measuring time?
Edit: Actually the site that I quoted for the acceleration of a fastball as 98m/s^2 has a similar error using d as the distance of the mound to the plate instead of just the arm motion. So I donât think thatâs correct. The real value is actually much higher. The massive numbers may actually be reasonable figures.
Sorry about that, something posted on internet is wrong. Who knew?
Put in the correct values for distance d and redo the calculations and let us know what you get.
one thing to consider is you are not âfollowing throughâ on the throw like a baseball pitcher would, so the comparison may not be an accurate one.
a baseball pitcher is trying to maximize velocity or speed with their pitch. a yoyoer, with their inclination to:
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stop short (as opposed to extending their arm completely), thereby preventing the yoyo shooting straight into the ground⌠and therefore continue with tricks
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a throwers tendency to not necessarily maximize the âspeedâ of their throw, but the âlength of timeâ of their throw, taking advantage of the yoyoâs moment of inertia, is why the baseball pitcher comparison may not be as appropriate
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the immediate âdeccelarrationâ referenced in the first bullet above, could be contributing to
the miscalculation
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Yes, the throw itself is going to be messy and harder to analyze. The descent on the string should be easier. Itâs a straight(er) motion, and I would expect the acceleration to be much more consistent. It does have a non-zero starting velocity, so you do have to take that into account.
The way I would analyze this is to make a position vs time graph, and fit a curve. You can also make a velocity vs time graph, and just look at the slope. If youâre filming at 240fps, you should have enough points. LoggerPro will generate these graphs for you. You just need to set up the scale with the string length, then click on the yoyo in each frame of the part of the video you are interested in.
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iâm not sure what loggerpro is, but it sounds like the OP may be trying to solve (or check the work) of a âdynamicsâ problem with a âstaticsâ solution.
there is not a moment in time (of the OPâs concern) that the âbodyâ is at rest where assumptions, variables, and then calculations can really take place from
a âstaticâ perspectiveâŚbodies are in motion⌠and iâd think checking work from a dynamics perspective may produce comparable (and accurate) results
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Thank you for your guysâ help. I redid the times, and I got results like 33 m/s^2, which make more sense. I have handed it in and have hoped for the best. Have a great day
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