Biomechanics I, somersault question using angular accel/ vel

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SUMMARY

The discussion focuses on the biomechanics of a diver performing somersaults from a height of 10 meters. The athlete can rotate at 5.7 rad/s in a tucked position, allowing her to complete approximately 1.28 somersaults before reaching 1 meter above the water. For the piked position, the diver performs 3 somersaults in the same time frame, necessitating a calculation of her angular velocity. Additionally, the diver transitions to a tucked position over 0.2 seconds, prompting the need to calculate her angular acceleration using the formula α = (w2 - w1) / (t2 - t1).

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Homework Statement


An athlete performs a dive from a handstand off a 10m tower. her center of mass is 0.8m above the tower as she falls into the dive

a) if she can rotate at 5.7rad/s in a tucked position, how many complete somersaults can she do in her dive? assume she must stop rotating 1m above the water to ensure clean entry

b) if she can perform 3 somersualts in a piked position in the same amount of time, what is her angular velocity when performing piked somersautls?

c) the diver is performing a piked dive. she realizes that she won't have enough time to finish her last somersialt and enter the water in a vertical position, so she moves into a tucked position over 0.2s. What is her anguar accel


Homework Equations


v2^2 = v1^2 + 2ad
v2 = v1 +at
angular vel = change in angular displacement / time
alpha = (w2 - w1)/ (t2 - t1)

The Attempt at a Solution


a) i used, v2^2 = v1^2 + 2ad to determine that v2 = - 13.87m/s 1m from the water
and then i used, v2 = v1 +at to determine it take t= 1.41s to reach 1m above water
can i use kinematic laws in this question, or does the diver's somersaults complicate the question?
i then used 5.7rad/s x 1.41s = 8.0569 rad
8.0569rad x 1somersault/2pie radians = 12.66 somersaults (12 complete somersaults)
*EDIT* 8.0569rad x1somersault/2pie rad = 1.28 somersaults (1 complete somersualt)

is it correct to do this?
or would the t = 1s since she has 9.8m to perform somersualts and gravity is -9.81m/s^2?

b) i tired to use, w = change is angular displacement/ t
is angular displacement 0 since she returns to the same position (3 full somersuats)?

c) i tried alpha = (w2 - w1)/ (t2 - t1)
i was going to plug in, 5.7rads/s for w2, and my answer in question b) into w1
and then t= 0.2s

any help would be appreciated =) thank you
 
Last edited:
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Be careful dividing by 2π using a calculator. 2π ≈ 6.3 . Certainly 8.1/6.3 ≠ 12.

I'm pretty sure what you did was 8.0569rad × 1somersault/2×π . Using order of operations, this is (8.0569rad × 1somersault/2)×π, so you multiplied by π, rather than dividing.
 
thank you
is it correct to apply linear kinetics laws to determine the answer for 1a)?
 
jklgfds120 said:
thank you
is it correct to apply linear kinetics laws to determine the answer for 1a)?

If you mean "Are angular (rotational) kinematics analogous to linear kinematics?", then, yes, you use them the same way.
 

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