Angular velocity from diving board

[lalahelp]

Homework Statement

A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.34 complete rotations in 1.23 s. If his rotational inertia decreases by a factor of 2.56 when he goes from the straight to the tuck position, what was his angular velocity when he left the diving board?

Homework Equations

I1W1=I2W2

The Attempt at a Solution

I don't know how to solve the problem using the equation, I am not sure how to plug in the information.

 

[cepheid]

Homework Statement

A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.34 complete rotations in 1.23 s. If his rotational inertia decreases by a factor of 2.56 when he goes from the straight to the tuck position, what was his angular velocity when he left the diving board?

Homework Equations

I1W1=I2W2

The Attempt at a Solution

I don't know how to solve the problem using the equation, I am not sure how to plug in the information.

You are given that I₁/I₂ = 2.56 (where I₂ is after the tuck, in the more compact position).

You can use the angular distance Δθ and time interval Δt that are given to calculate the angular speed ω₂ of the diver during the tuck.

 

[lalahelp]

so I do (2.56)W1=W2


W1 is V/R
How do I do that part?

 

[cepheid]

so I do (2.56)W1=W2W1 is V/R
How do I do that part?

Again, just like I said before, you can solve for ω₂ because you are given angular distance and time, and therefore you can find the angular speed. Once you know ω₂, you can use the conservation of angular momentum equation that you wrote above to find ω₁, which is what the problem is asking for.

 

[asteriatic]

However, I can explain the concept behind the solution.

Angular velocity is the rate at which an object rotates around an axis. In this case, the diver is rotating around his own axis while in the air. The rotational inertia, or moment of inertia, is a measure of an object's resistance to change in its rotation. When the diver pulls himself into a tuck position, his rotational inertia decreases due to the change in his body's distribution of mass.

To solve this problem, we can use the equation I1W1=I2W2, where I1 and W1 represent the initial rotational inertia and angular velocity, and I2 and W2 represent the new rotational inertia and angular velocity after the tuck position is assumed. We know that the rotational inertia decreases by a factor of 2.56, so we can set up the equation as:

I1W1 = (1/2.56)I1(W2)

We also know that the diver completes 2.34 rotations in 1.23 seconds, so we can plug in these values for W1 and W2:

I1(2.34/1.23) = (1/2.56)I1(W2)

Solving for W2, we get:

W2 = 2.34(2.56)/1.23 = 4.88 rad/s

Therefore, the diver's initial angular velocity when leaving the diving board was 4.88 rad/s.