Uniform Circular Motion NS FL #2

[agileduck]

One of the questions on NextStepTestPrep's Full Length MCAT #2 Physical Sciences Section has got me stumped. It's about uniform circular motion, and in the explanation the formula they give doesn't make sense.

As far as I know the formula should be v=2pir^2/T, but instead they have written v=2pir/T. This, of course,
throws off the whole calculation.

If we use the first formula v= 15 m/s, which we plug into the Fc equation getting 1650 N.
However, without squaring v=3.14 m/s, giving a total of 100 N.

I have attached screenshots!

---

Members don't see this ad.

 

[BerkReviewTeach]

You should probably start by looking at the AAMC Official Guide in terms of topics that are tested. While this topic was fair game before 2015, and can be found on their older list, it does not appear now. Consult pages 169 through 173 for a complete list, and in particular page 170 where a topic like this would have fit (if it was on their list).

To be fair, people have mentioned in the past that some topics not on that list have loosely fit into other categories, but it seems like the closest thing here would be torque, and that is a tiny subtopic in their listing under Equilibrium.

 

[NextStepTutor_2]

One of the questions on NextStepTestPrep's Full Length MCAT #2 Physical Sciences Section has got me stumped. It's about uniform circular motion, and in the explanation the formula they give doesn't make sense.

As far as I know the formula should be v=2pir^2/T, but instead they have written v=2pir/T. This, of course,
throws off the whole calculation.

If we use the first formula v= 15 m/s, which we plug into the Fc equation getting 1650 N.
However, without squaring v=3.14 m/s, giving a total of 100 N.

I have attached screenshots!


View attachment 202786 View attachment 202787

Hi @agileduck !

Do NOT make the mistake of being a slave to the explicit text in the AAMC outline. Too many people forget to take into the account how liberal the AAMC is with their topic headings, and always have been. This topic fits right into 4A , can and has been tested under kinematics and Newtonian mechanics . In fact AAMC reps I have spoken with, as recently as Feb 2016 say that projectile motion, not listed explicitly either, fits in here as well. UCM would not fit in with torque directly as torque refers to causing rotational motion (where the center of mass generally doesn't have to move) while UCM certainly fits right in with translational motion, Force, Equilibrium and Work (objects undergoing UCM have no net work done on them). The AAMC is not out to spoon feed you, do not take the outline as an exhaustive list of ways they will test you on a given topic. These concepts are fair game in the new AAMC material. In addition, if you want to understand how an MRI works, or
how particles will move in a uniform electric of magnetic field, you better understand UCM.

For this question, you are given frequency and radius of the merry-go-round. Frequency , given is 0.1 Hz is cycles/sec, where 1 cycle = 1 complete rotation of the merry-go-round. Frequency = 1/period so period (T) = 1/0.1 = 10 seconds. This tells us the merry-go-round takes 10 seconds to complete 1 full rotation.

Each complete rotation means a point on the edge of the circle/merry-go-round has traveled a distance equal to the circumference of the circle. Circumference = 2*pi*radius. Thus they are telling us this circle spins at 2*pi*radius every 10 seconds.

2*pi* 5/10 = 2*3*5/10 = 30/10 = 3 m/s

Next we use the equation for centripetal force (center seeking force) F = mv^2/r

F = 50(3^2)/5 = 50(9)/5 = 90 N. We rounded pi down to an even 3 so the answer should be a bit bigger than 90 N, Choice B.

Perhaps you are confusing circumference ( 2*pi*r) with Area of a circle (pi*r^2) ??

Hope this helps, good luck!