Question

1 a. A man spinning on a stool while holding two heavy books in each hand. What happens when he pulls his arms towards his chest when still holding the books? Why? What properties are conserved and what properties change?

b. when doing sit ups, is it easier to have your hands behind your head or extende straight over the head(like when you are going to dive) ? why?

Answer 1

a) When he pulls his arms towards his chest, his speed of spinning increases.
It's caused by conservation of angular momentum.
Like linear momentum (mv), angular momentum (r×mv) is a conserved
quantity, where r is the vector from the center of rotation. For him
holding a static pose, for each particle making up his body, the
contribution in magnitude to the total angular momentum is given by
mirrvi. Thus bringing in his arms reduces ri for those particles. In
order to conserve angular momentum, there is then an increase in the
angular velocity.
Momentum is conserved, energy changes.