Consider a turntable to be a circular disk of moment of inertia it rotating at a constant angular velocity ωi around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). the axis of the disk is vertical and the disk is supported by frictionless bearings. the motor of the turntable is off, so there is no external torque being applied to the axis. another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). the moment of inertia of the record is ir. the initial angular velocity of the second disk is zero. there is friction between the two disks. after this "rotational collision," the disks will eventually rotate with the same angular velocity.

Note: Angular momentum is always conserved in a collision.

The initial angular momentum of the system is

L = ( It ) ( ωi )

where It = moment of inertia of the rotating circular disc,

ωi = angular velocity of the rotating circular disc

The final angular momentum is

L = ( It + Ir ) ( ωf )

where ωf is the final angular velocity of the system.

Since the two angular momenta are equal, we see that

( It ) ( ωi ) = ( It + Ir ) ( ωf )

so making ωf the subject of the formula

ωf = [ ( It ) / ( It + Ir ) ] ωi

Explanation:

the answer would be c. motion and direction

i hope this : )

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.