TBR Circular Motion 25 Review Question #23

[argama]

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The question says that "If a person starts at the rim of a spinning platform and is pushed radially toward the central axis by a moving exterior wall, what happens to the normal force felt by the person due to the wall?"

A. constant
B. decreases b/c R decreases
C. increases b/c R decreases
D. increases since Angular Speed decreases


So I chose C but the Answer was B. I reasoned that Fnormal is proportional to the centripetal acceleration but I was thinking of the formula a = v^2/R so I said that Fnormal would increase since R decreased. But the answer says that Fnormal decreases since acceleration also equals a = w^2R so by decreasing R, acceleration decreased, thus Fnormal decreased.

So my question is: Which formula was "correct" and when do I know which to use? both are for centripetal acceleration so I found this confusing 🙁

Thanks!

 

[osprey099]

The question says that "If a person starts at the rim of a spinning platform and is pushed radially toward the central axis by a moving exterior wall, what happens to the normal force felt by the person due to the wall?"

A. constant
B. decreases b/c R decreases
C. increases b/c R decreases
D. increases since Angular Speed decreases


So I chose C but the Answer was B. I reasoned that Fnormal is proportional to the centripetal acceleration but I was thinking of the formula a = v^2/R so I said that Fnormal would increase since R decreased. But the answer says that Fnormal decreases since acceleration also equals a = w^2R so by decreasing R, acceleration decreased, thus Fnormal decreased.

So my question is: Which formula was "correct" and when do I know which to use? both are for centripetal acceleration so I found this confusing 🙁

Thanks!

I think it's B because for this situation, you use a = w^2R because w (omega) does not change. Omega is a measure of the change in pheta (angle) and since you are pushing inward, you are not changing pheta so omega stays constant. If you use a = v^2/r on the other hand, you do not know whether v (tangential velocity) increased or decreased or stayed the same so you cannot assume it stayed constant and the formula would not be appropriate in this situation. In terms of knowing what formula to use, think about what variables you know that stays constant and what variable you know that changes. Try to find a formula that has all constant variables except for the non-constant variable that you are looking for.