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Question

A diver performing a double somersault spins at an angular speed of 4.0 $ rad/s precisely 0.50 s after leaving the platform. Assuming the diver begins with zero initial angular speed and accelerates at a constant rate, what is the diver’s angular acceleration during the double somersault?

Answer 1

Going into the somersault, for the first 0.5s:
accel = dV/dt = 4 rad/s / 0.5s = 8 rad/s/s

In the somersault, t>0.5, the angular velocity is constant, thus
accel=0

Note that 8 rad/s is an incomplete answer. The double somersault does not stop at 0.5s. The answer should be:
8 rad/s/s for t< 0.5
0 rad/s/s for t>0.5

Since it is a double somersault so:you need to do 4pi rad (two revolutions).

During the accelerating part the radians traveled, Rt, is given by:
Rt = Rt(t=0) +angVel(t=0)*t + 0.5*A*t^2
= 0 + 0*t + 0.5*(8 rad/s/s)* (0.5s)^2 = 1 rad

You still have (4pi-1) radians left to complete the double somersault. Now you are traveling 4 rad/s. The remaining time is given by:
Rt(t=tFinal) = Rt(t=0.5)
+ angVel(t=0.5)*(t-0.5)
+0.5*A*(t-0.5)^2
Or,
4*pi rad = (1 rad)
+ (4 rad/s)*(tFinal-0.5s)
+ 0.5*0*(t-0.5s)^2

Solving for tFinal
tFinal = (4*pi rad - 1 rad)/(4rad/s) + 0.5s
= 3.39 s

The complete answer is:
8 rad/s/s for t< 0.5
0 rad/s/s for 3.39s>t>0.5

Sounds like a long dive? Maybe i have an error, or maybe that $ means something. Either way you need the complete dive for a complete answer.

Answer 2

As I'm sure you know, acceleration is just change in velocity / change in time, the same goes for angular velocity and time is a constant. Sooooooooooo...

Seeing as he started from 0 rad/s "Assuming the diver begins with zero initial angular speed." and "spins at an angular speed of 4.0rad/s"

Then 4.0 rad s ^-1 / 0.5s = 8 rad s^-2 = Angular acceleration.

Answer 3

w = alpha t; where alpha = average angluar acceleration, which you are looking for, w = angular velocity = 4 rad/sec, and t = 1/2 sec the elapsed time from when starting the somersault. Therefore alpha = w/t = 4 rad/sec//1/2 sec = 8 rad/sec^2.

Note the similarities between w = alpha t for angular velocity and v = at for the linear version of velocity with a the linear acceleration..

Answer 4

i really feel sorry for u, i am so glad i do not have to think about physics for another week.