Biomechanics I, somersault question using angular accel/ vel

[jklgfds120]

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

 

[SammyS]

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.

 

[jklgfds120]

thank you
is it correct to apply linear kinetics laws to determine the answer for 1a)?

 

[SammyS]

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.

 

[rwisz]

I would first like to commend you for your attempt at solving this problem using the appropriate equations and concepts from biomechanics. Your approach is generally correct, but there are a few areas where you can make some improvements.

a) Your use of the kinematic equations is appropriate. However, there is a mistake in your calculation for the number of somersaults. The formula for angular velocity (w = change in angular displacement / time) assumes that the object is rotating at a constant rate. In this case, the diver's angular velocity is not constant, as she must stop rotating 1m above the water. Therefore, you cannot simply multiply her angular velocity by the time it takes to reach 1m above the water to get the number of somersaults. Instead, you should use the formula for angular displacement (theta = w*t) to determine the total number of radians she rotates in the dive. Then, divide this by 2*pi radians to get the number of complete somersaults.

b) Again, your use of the formula for angular velocity is correct. However, as mentioned in part a), the diver's angular velocity is not constant. Therefore, you cannot use this formula to determine her angular velocity during piked somersaults. Instead, you should use the formula for angular displacement (theta = w*t) to determine the total number of radians she rotates in the piked dive. Then, divide this by the time it takes to complete 3 somersaults to get her average angular velocity during piked somersaults.

c) Your approach using the formula for angular acceleration is correct. However, as mentioned in part b), the diver's angular velocity is not constant. Therefore, you cannot use the formula for angular acceleration (alpha = (w2 - w1)/(t2 - t1)) to determine her angular acceleration during the transition from piked to tucked position. Instead, you should use the formula for angular velocity (w = change in angular displacement / time) to determine her angular velocity during the transition. Then, use the formula for angular acceleration to determine her angular acceleration.

Overall, your understanding of the concepts and equations involved in biomechanics is good. However, it is important to carefully consider the assumptions and limitations of each formula in order to apply them correctly. Keep up the good work!