Please help me

[piper210_355]

I need help with this problem. My teacher gave it to us but I'm not sure how to proceed.

 

The tape in a standard VHS cassette has a otal length of 246m, which lasts for 2.0 hr. As it starts the full reel has a 45mm outer radius and a 12 mm inner radius. At some point during the play both reals have the same angular speed. Calculate the angular speen in rads/sec and in revs/min.

 

Hint: Between the two reels the tape moves at a constant speed

 

 

My teacher said we might find these equations helpful:

W=R/R(f) W is angular velocity

V=L/t

πr^2=.5(πR^2-πr^2)

 

 

I know I have to convert 2.0 hr to 7200 secs.

If I use the second equation she gave then I get

V= 246/2=123

 

I know how to convert rads/sec to revs/min, I just don't know where to start with the problem.

[Jacques]

First thing I would do to simplify the problem is to convert everything in the same units.

For time you have hour and you have sec and minute. For the lenght you have meter and millimeter. I would suggest to convert every thing in millimeter and second.

After I would do some exercise: What is the angular speed in rads/sec at the beginning of the tape ? at the end of the tape ?

You will see that the angular speed depend on the radius of the reel.

So the sub-question: What is the radius of the reels when they have the same angular speed ? Answer: When they have the same radius. What is that radius ?

That were you need more thinking

[piper210_355]

ok so i did the conversions

I don't know what equation to use for the angular speed though.

I'm currently working on finding the radius when the angular speed is the same, but i'm not sure how to do that either

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i saw in one site that the equation for angular speed is v/r=w

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ok so with that equation it think I can do your exercise questions:

at the begining r=45 so

w= (123)/45=2.73

 

in the end there is no tape on the reel so r=12 and

w=123/12=10.25

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so what do i do to find out when the radius is the same?

Edited January 27, 2009 by piper210_355
Consecutive posts merged.

[Jacques]

246000 mm / 7200 sec = 34.17 mm/sec

That the linear speed of the tape.

34.17/45 = .76 rad/sec at the beginning when the reel is full

 

the trick to find the radius when the angular speed is the same is to think in term of surface. The tape has a thickness and the area of the tape is constant.

At half the tape the total area of the tape on the 2 reels is the same has the area of the tape on the big reel at the beginning.

pi*R^2-pi*r^2=pi*(R^2-r^2)=pi*(45*45-12*12)=5909 mm^2

Half that is 2954.5

2954.5=pi*(x*x-12*12) where x is the radius of the reel half way