Homework EquationsN/A The Attempt at a SolutionN/A

In summary, a first year biomechanics student is struggling with a problem involving a 60kg diver who has an initial angular velocity of 14rad/sec and a radius of gyration of 0.5m. The student is confused about how to solve the problem without a "change in time" in the equation. However, it can be solved using conservation of angular momentum and the given information of the diver's mass and altered radius of gyration of 0.3m.
  • #1
jayty22
1
0
angular velocity?!

Homework Statement


Hello, I am a 1st yr biomechanics student and I am having a lot of problems figuring this stuff out and I have an exam coming up and I'm kinda panicing! lol! ok here is the exact problem:

"A 60kg diver is positioned so that his radius of gyration is 0.5m as he leaves the board with an angular velocity of 14rad/sec. What is the diver's angular velocity when he assumes a 'tuck' position, altering his radius of gyration to 0.3m?"

My conundrum comes because the formulas we were given all include a 'change in time' to be used in the equation. Maybe (yes, definately!) I am missing something here so can someone please educate me as to how I would go about solving this problem and the formula that I am supposed to use.

Thanks very much in advance,

- One confused young man (a.k.a. Jay) :confused:
 
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  • #2
Giving you the radius of gyration and the mass is a way of giving you the moments of inertia (and I had to look that up). Think about conservation of angular momentum.
 
  • #3


Homework Equations
N/A

The Attempt at a Solution
N/A. angular velocity?!

Hi Jay, first of all, don't panic! Biomechanics can be a challenging subject, but with some effort and practice, you can understand it. Let's take a look at this problem together.

The initial angular velocity of the diver leaving the board is 14 rad/sec. This means that he is rotating at a rate of 14 radians per second. Remember that angular velocity is a measure of how fast an object is rotating, just like linear velocity is a measure of how fast an object is moving in a straight line.

Now, the diver changes his position and alters his radius of gyration to 0.3m. This means that his body is now rotating around a smaller radius, which will affect his angular velocity. In order to calculate his new angular velocity, we need to use the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

In this case, the diver is the system and he is not experiencing any external torques, so his angular momentum remains constant. The formula for angular momentum is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

We can rearrange this formula to solve for ω: ω = L/I. Since we know that the diver's initial angular momentum is equal to his final angular momentum, we can set up the equation: I1ω1 = I2ω2, where I1 and ω1 are the initial values and I2 and ω2 are the final values.

We know that the moment of inertia is related to the radius of gyration by the equation I = mk^2, where m is mass and k is radius of gyration. So for the initial position, we have I1 = mk1^2 and for the final position, we have I2 = mk2^2.

Substituting these values into our equation, we get mk1^2ω1 = mk2^2ω2. We can now solve for ω2: ω2 = (mk1^2ω1)/(mk2^2). Since we are given the values of k1 = 0.5m, k2 = 0.3m, m = 60kg, and ω1 = 14rad
 

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