##### Physics Question on angular speed

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It has been suggested that rotating cylinders about 16.5 mi long and 3.69 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Oct 12th, 2015

Ok first thing to do is since this involves gravity, is to set everything to metric units

Dimensions of the cylinder

L=26554.18 m

D= 5938.48 m

Now to solve for the angular velocity, we write the acceleration as a function of the cylinder radius R and w, and set it equal to the acceleration due to gravity.

Oct 12th, 2015

checking the answer I derived

Oct 12th, 2015

w= angular speed R= radius D/2  g=9.81m/s^2

w= 9.81 m/s^2/*(5938.48 m / 2)

w= .003 /s^2

Oct 12th, 2015
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Why do you use the diameter number, not the length?

Oct 12th, 2015

Because the angular speed for a rotating cylinder is related to it's radius (1/2 the diameter) and not the length.

Oct 12th, 2015

How do you concert from s^2 to rad seconds

Oct 13th, 2015

I had a typo. How to convert that answer to rad/sec?

Oct 13th, 2015

multiply the answer by 1/(2*pi)

Oct 13th, 2015

Did you get 0.005??

Oct 13th, 2015

Sounds correct and yes

Oct 13th, 2015

It not right. Its mark wrong on my homework page

Oct 13th, 2015

Hmm i'm checking the notes I have, it's possible the square root of the first answer we got needs to be taken at the end to get the correct answer.

Oct 13th, 2015

I have no idea. Lol. Physics isn't my strong sute

Oct 13th, 2015

Try the answer .055 rad/s , according to a guide it took similar steps we did besides taking a square root at the end, and if that doesn't work I'll try to find a better equation

Oct 13th, 2015

Yeah .055 should be correct

According to a guide

So the fixed derivation was

Oct 13th, 2015
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It's my last try, ok. Let me try

Oct 13th, 2015

Whow. That worked. How did you get that answer? Thanks so much for your help.

Oct 13th, 2015

Yes we did it ^, I was just following the fixed version of their equation I didn't find an exact derivation of where it came from out of what I read before

I remember looking for more answers the centripetal acceleration I saw was

V^2/R=g

but there was one more relation that fixes it to get their equation, found something just now

Oct 13th, 2015
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A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 290 Napplied to its edge causes the wheel to have an angular acceleration of 0.872 rad/s2.

a) What is the moment of inertia of the wheel? 107.9 kg · m
This is correct on my homework.
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b) What is the mass of the wheel?

Oct 24th, 2015

Humans can bite with a force of approximately 797 N. If a human tooth has the Young's modulus of bone, a cross-sectional area of 1.2 cm2, and is 1.7 cm long, determine the change in the tooth's length during an 7.97 ✕ 102 N bite.

Nov 8th, 2015

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Oct 12th, 2015
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Oct 12th, 2015
Dec 11th, 2016
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