Question

During a trampoline routine, a gymnast is tumbling in the air at 20 rad/s in a tuck position. He then extends into a layout position and doubles his radius of gyration just before landing on the trampoline bed. How fast is his angular velocity at this instant, just before landing on the trampoline bed? Group of answer choices 5 rad/s 10 rad/s 5 m/s 4 rad/s 80 rad/s

Answer 1

`\omega = 5 rad/s`

Step-by-step explanation:

As we know that the gymnast has no external torque on it

so here we can say that angular momentum of the system will be conserved

so here we have

`L_1 = L_f`

`I_1\omega_1 = I_2\omega_2`

`m_1r_1^2\omega_1 = m_1r_2^2\omega`

`r_1^2\omega_1 = r_2^2\omega`

here we know that

`r_2 = 2r_1`

`r_1^2\omega_1 = (2r_1)^2\omega`

`20 = 4\omega`

`\omega = 5 rad/s`