During her dismount from the balance beam, a gymnast experiences a ground reacti

Question

During her dismount from the balance beam, a gymnast experiences a ground reaction force of 2242 N that passes within a minimum distance of 0.32 m from her center of mass and lasts for 0.188 s. At the end of that time she leaves the beam and her moment of inertia is 7.3 kg m2. During that 0.188 s the force and line of action of the force with respect to the center of mass are constant. Prior to that final 0.188 s her angular momentum was zero. What will be her angular velocity in units of rad/s when she leaves the beam?

Explanation / Answer

torque = r x F = I x alpha

0.32 x 2242 = 7.3 x alpha

alpha = 98.28 rad/s^2

angular acceleration is 98.28 rad/s^2 and initial angular velocity was zero.

Using wf = wi + (alpha*t)

wf = 0 - (98.28 x 0.188)

wf = 18.48 rad/s

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