A diver performs a dive starting from a handstand off a 10.0-meter platform. What is her average angular velocity during the dive if she completes exactly 3 revolutions before she hits the water?
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I think I know how they want you to do this problem:
calculate the time it takes for a diver to fall 10m and then calculate angular velocity from
angular velocity = 3x2 pi radians/time to fall 10 m
and this is what you want to do, but they don't give you enough information to calculate the time to hit the water
because a human being is not a point mass and is by definition rotating, the diver has both translational and rotational kinetic energy
this means that the total linear (translational speed) toward the water is not the same as it would be for a crate dropped from 10m
you could find the final translational speed if you knew the moment of inertia of the diver, but they don't give you enough information for that...so...they way they want you to solve this is:
height = 1/2 gt^2 or t = Sqrt[2h/g] = Sqrt[2 x 10m/9.8m/s/s] = 1.43s
and ang velocity = 3x(2 pi rad)/1.43s = 13.2 rad/s
but the actual answer will be less than that since some of the initial potential energy of height while standing on the platform will go into rotational KE and not just translational KE
calculate the time it takes for a diver to fall 10m and then calculate angular velocity from
angular velocity = 3x2 pi radians/time to fall 10 m
and this is what you want to do, but they don't give you enough information to calculate the time to hit the water
because a human being is not a point mass and is by definition rotating, the diver has both translational and rotational kinetic energy
this means that the total linear (translational speed) toward the water is not the same as it would be for a crate dropped from 10m
you could find the final translational speed if you knew the moment of inertia of the diver, but they don't give you enough information for that...so...they way they want you to solve this is:
height = 1/2 gt^2 or t = Sqrt[2h/g] = Sqrt[2 x 10m/9.8m/s/s] = 1.43s
and ang velocity = 3x(2 pi rad)/1.43s = 13.2 rad/s
but the actual answer will be less than that since some of the initial potential energy of height while standing on the platform will go into rotational KE and not just translational KE