Physics normal force rotation fun yeah!

[chiddler]

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Note that the space station is a giant rotating cylinder. If a person starts at the rim of a space station and moves radially towards the center axis in an elevator, what happens to the normal force felt by that person?

A. Constant.
**B. Decreases since radius decreases.
C. Increases since radius decreases
D. Decreases, since angular speed decreases

My incorrect reasoning is as follows:

When you're on the ground, normal force is mg. Here, radius is decreasing. According to a = v^2 / r, acceleration will increase, and normal force increases.

So. Is the increasing acceleration = the artificial gravity or is this acceleration = rotational? And I would appreciate an explanation for the question, please.

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How long will it take a person to complete one revolution? Radius is 1000m and tangential speed is 300 m/s.

I tried using ω = v / r but i'm not sure how to convert 300 m/s to rev/sec.

Many thanks!

 

[MedPR]

Note that the space station is a giant rotating cylinder. If a person starts at the rim of a space station and moves radially towards the center axis in an elevator, what happens to the normal force felt by that person?

A. Constant.
**B. Decreases since radius decreases.
C. Increases since radius decreases
D. Decreases, since angular speed decreases

My incorrect reasoning is as follows:

When you're on the ground, normal force is mg. Here, radius is decreasing. According to a = v^2 / r, acceleration will increase, and normal force increases.

So. Is the increasing acceleration = the artificial gravity or is this acceleration = rotational? And I would appreciate an explanation for the question, please.

-------

How long will it take a person to complete one revolution? Radius is 1000m and tangential speed is 300 m/s.

I tried using ω = v / r but i'm not sure how to convert 300 m/s to rev/sec.

Many thanks!

Nice to know I'm not the only one studying on Christmas eve.

Question 1: I have no idea.
Edit: For number 1, I would assume you have to use a = w^2r since the person is moving radially and w is the angular velocity. In that equation, as r decreases, a decreases, thus decreasing normal force.
Question 2: One revolution = circumference = 2pi * radius = 2000pi. w = theta/t. so t=2000pi/300 = ~20seconds.

 

[Pisiform]

Whenever the radius changes, tangential velocity also changes. In circular motion, only time taken to go around a circle remains constant regardless of the radius. So in this case you will use Ac = (omega)^2 r ... so as r decreases ... a_centripetal decreases

300m/s .... R = 1000m

1 rev === 2 pi r = 2 pi 1000 = 6283m

300m --- 1 sec
6283m ---- 20.9sec

 

[chiddler]

What is the difference between the two formulas:

a = v^2 / r

a = ω^2 * r

specifically how did you guys know to use the second one? each would give opposite results.

 

[MedPR]

What is the difference between the two formulas:

a = v^2 / r

a = ω^2 * r

specifically how did you guys know to use the second one? each would give opposite results.

Because w is angular velocity and v is linear velocity. v is tangential only, w is along the arc length.

 

[chiddler]

Because w is angular velocity and v is linear velocity. v is tangential only, w is along the arc length.

thanks a lot.

 

[MedPR]

thanks a lot.

Haha, sorry I realize now that my original answer wasn't very clear.

You can use a=v2/r, but you have to realize that both v and r are changing when the radius decreases (or increases). Since v is tangential velocity, as you decrease r, you also decrease v. Remember that if you decrease the radius, you decrease the circumference of the circle, thus decreasing the distance of one revolution. x=vt, so decreasing the distance means decreasing velocity.

It's easier to use a=w2r because w doesn't change as the circumference changes since the definition of w is w=2pi/t.