What is the speed of the skaters in this case? 
You're choreographing your school's annual ice show. You call for eight 60kg skaters to join hands and skate side by side in a line extending 12m. The skater at one end is to stop abruptly, so the line will rotate rigidly about the skater. For safety, you don't want to fastest skater to be moving at more than 8.0 m/s, and you don't want skater's hand to exceed 300N. What do you determine is the greatest speed they can have before they execute their rotational maneuver? 

This question is from my physics book and I can't seem to get the answer right which is supposed to be 5.5 m/s.
What I have been doing is equating initial angular momentum: $mvr$ to the final angular momentum: $\frac{1}{3}mL^2\cdot \omega_f$
But I am not using the force and it's giving me a wrong answer
 A: Using the conservation of angular momentum is great.  The safety limits are at risk of being exceeded while the line is rotating, not while it is going straight, so you will work backward from the maximum safe rate of rotation.  There are two speed limits, and you will need to compute both and choose the most conservative one:


*

*The fastest skater can't exceed 8 m/s.  This should be pretty straightforward.  (the fastest skater is the one on the outside...)

*The force applied by any skaters hand can be at most 300 N.  Which skater is going to have the greatest force on their hand?  You will need to assume that the skates exert no frictional force in any direction (except for the stationary skater, who we will consider to have "dug in" his skates...).  Draw free body diagrams for the skater on the outside, one of the middle ones, and the one on the inside.  Don't forget that all but one of the skaters are accelerating during the turn.


If you have ever played (or even just read about) the children's game "crack the whip", you might be dissatisfied by the result that the greatest hand force is on the inside rather than the outside.  This discrepancy between the problem and reality is caused by the assumption that the line rotates rigidly, which is flagrantly incompatible with the assumption of no lateral skate force, which is necessary to get an answer from such scant information.
