Question

A gymnast dismounts off the uneven bars in a tuck position with a radius of 0.3m (assume she is a solid sphere) and an angular velocity of 2rev/s. During the dismount she stretches out into the straight position, with a length of 1.5m, (assume she is a uniform rod through the center) for her landing. The gymnast has a mass of 50kg. What is her angular velocity in the straight position?

Answer 1

Here we will say that there is no external torque on the system so we will have

`L_i = L_f`

here we know that

`L_i = I_1\omega_1`

where we know that

`I_1 = (2)/(5)mr^2`

Also we know that

`I_2 = (1)/(12)mL^2`

initial angular speed will be

`\omega_1 = 2\pi(2rev/s) = 4\pi rad/s`

now from above equation

`(2)/(5)mr^2 (4\pi) = (1)/(12)mL^2 \omega`

`0.4(0.3)^2(4\pi) = (1)/(12)(1.5)^2\omega`

`0.452 = 0.1875 \omega`

now we have

`\omega = 2.41 rad/s`

so final speed will be 2.41 rad/s