Question

A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3.00 to 4.10 rev/s while rotating through two-thirds of a revolution. How much time does this maneuver take?

Answer 1

Given data :-

Initial angular velocity (_i) = 3 rev/sec

Final angular velocity (_f) = 4.10 rev/sec

Angular displacement () = 2/3 (or) 0.666 rev

Time required (t) = ??

Formuale :-

Relation between angular displacement() & average angular velocity(_avg) with time(t) is :-

= (_avg) * t

Time (t) = / ( _avg ) ----------------- Equation

where _avg = 0.5*(_i + _f)

_avg = 0.5*(3+4.1)

_avg = 3.55 rev/sec

Substitute the given values in above equation

we get ;

Time (t) = 0.666/3.55

t = 0.187 sec

Hence the maneuver takes time (t) = 0.187 sec