Need solutions for the checkpoint questions in the slide show for Physics I : (fall 2010)

Question

experimentx · Answer

could you point out particular problem?

anonymous · Answer

These 2 questions please

experimentx · Answer

I think you need to use the conservation of angular momentum for first question.

anonymous · Answer

We are expected to do the question from  the concept of work 
just before this question they explained about dot product.

experimentx · Answer

what force do you have to apply to bring that rotating ball closer?

experimentx · Answer

it's centripetal force ... he centripetal force is given by 
$$ F = mv^2/r$$ 
to bring it to R_1 distance from R_2
$$ \int_{R_2}^{F_1} F \cdot dr $$ 
Now equate this thing with KE.

anonymous · Answer

$$mv ^{2}\ln (r2/r1)=mv ^{2}/2$$
 m, v2 cancels 
giving $$\ln (r _{2} div r _{1})=0.5$$
so, it is independent of v;
thus, v should remain constant

am i correct experimentX

experimentx · Answer

hmm .. no
mvr = J <-- this is constant.
so v will be function of 'r'

anonymous · Answer

how did u arrive to this conclusion need a step by step guide

experimentx · Answer

hmm ... we know that angular momentum remains converged ... no matter what.

anonymous · Answer

angular momentum is mvr which should be cpnsta
got it
thanx