The tape is now wound back into the drum at angular rate omega(t). with what speed will the end of the tape move? (note that our drawing specifies that a positive derivative of x(t)implies motion away from the drum. be careful with your signs! the factthat the tape is being wound back into the drum implies that \omega(t) < 0, and for the end of the tape to move closer to the drum, it must be the case that v(t) < 0.
answer in terms of omega(t) and other given quantities from the problem introduction.
v(t) =

See description

Explanation:

Frist we need to know the longitude of tape which is unwinding. Such relationship can be obtained with arc length. An arc length is the distance bewteen two points in a curve.

The relationship is:

Where is the arc length or distance, theta is the angle that results from the initial point of the measure to the final point, and r is the radius of a circumference.

Now let be length the unwinded tape. Change by and you ge the relationship:

if you unwind the tape by one revolution () you get the perimeter of a cricle , if you unwind it two times then and so on.

Then we have that the derivative of is

so we replace:

the derivative of theta with respect to t is ω(t) by definition:

The result is the relationship between angular velocity and the velocity and tangential velocity at the point r

we can see how the government has failed them.

i dont think you are wrong for wanting to get even with someone who did you wrong.

(i'm an eye for an eye kind of person) but if this person hurt you in a sexual way, i dont suggest doing anything to him. he should be taken to the proper authorities, you could go to jail depending on what you do. if it was something small like your sibling took your spot on the couch, than yea, i would get even with him by taking one of his favorite snacks lol. but i dont suggest you doing anything illegal.