# HOMEWORK

Okay, i can’t get the survey plugin to work and it’s canada day.

so. Post your answers in the Comments part, and i’ll get back to you and if you get the second question right i’ll give you a prize.

QUESTION: if you’re standing on a skateboard pointing east and west, which way do you roll if you take into account the rotation of the earth?

Answer: what kind of question is this ben? the language is imprecise and stupid. also, it’s terrible. the answer is “you stay still”.

REAL QUIZ QUESTION: suppose the earth is a perfect sphere, and it’s rotating (towards the east). and you are standing in the northern hemisphere. and you’re standing still. and you put down your skateboard just to the north of you, pointing east-west. and then you step onto your skateboard. which direction do you roll on account of the world’s turning?

### 4 Responses to HOMEWORK

1. Jacob 2 July, 2010 at 10:29 am #

Is that a frictionless skateboard?

:-p

• ben 2 July, 2010 at 7:27 pm #

yes

2. Jacob 6 July, 2010 at 6:10 am #

So here are the 3 possible answers to the question, from my perspective… Feel free to delete this comment if you’d rather let the listeners have a crack at it.

1)If the skateboard is frictionless, and the Earth is NOT spinning when the skateboard is placed on the ground (which is what I believe the listener asked), then once the Earth starts spinning to the East, the skateboard will remain stationary with respect to the original stationary Earth, which will give the appearance of rolling West on the Earth.

2)If the skateboard is frictionless, but is set down while the Earth is already spinning, then it will remain stationary with respect to the spinning Earth, and won’t “roll” at all. This is because the skateboard’s angular momentum around the center of the Earth doesn’t change from the moment the skateboard is set on the ground with respect to the moment before it. There are no external forces applied except for gravity and the centripetal force, which both act orthogonal to the direction of “roll”. And since an object in motion tends to remain in motion, the skateboard will “remain in motion” by continuing to travel along with the surface of the Earth, to the East, without “rolling” at all.

3) The skateboard is NOT frictionless, and the Earth starts from a stationary position. This one is tricky, because there’s a difference between static friction (how much force it takes to start the wheels turning) and kinetic friction (how much force it takes to keep the wheels turning).
In this case, once the Earth starts spinning, the skateboard will resist rolling at first until the static friction limit is reached, and will then start rolling similarly to answer #1. However, due to kinetic friction, the skateboard will not remain stationary with respect to the stationary Earth, but will instead move to the East with the rotation of the Earth, but at a slower rate than the spinning of the Earth. In other words, if you painted the spot where the skateboard started, and tracked both the skateboard and the painted spot, the painted spot would travel to the East faster than the skateboard would, such that the skateboard would appear to be traveling towards the West; however in reality, it is slowly traveling towards the East.

How’s that? I think that covers it, but I haven’t drawn any FBD’s or done any calcs, so I may be leaving out an effect of angular momentum…

Btw Ben, I’ve got another good one for you later ;-) Straight out of engineering school.

3. ben 6 July, 2010 at 6:22 am #

very good. was 1) what the reader asked? ok, then. It was clear to me that i got all caught up with overthinking things from the get-go.

In any case, your answers are all correct if you set your skateboard down to the east or west of you. but if you set it NORTH, you’ll start rolling EAST, and if you set it down to the SOUTH of you, you’ll start rolling WEST. :p

hit me with your engineering question!