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?

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.

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 wasAnswer: sqrt(.003)=.055 rad/s

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/s^{2}.

a) What is the moment of inertia of the wheel? 107.9 kg · m^{2 } This is correct on my homework. (

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 cm^{2}, and is 1.7 cm long, determine the change in the tooth's length during an 7.97 ✕ 10^{2} N bite.