Need help with a physics problem.

[CraKaJaX]

Question:

A wheel with a radius of 45.0 cm rolls without slipping along a horizontal floor. At time t1, the dot P painted on the rim of the wheel is at the point of contact between the wheel and the floor. At a later time t2, the wheel has rolled through one-half of a revolution.

What are:

a) the magnitude
b) the angel (relative to the floor) of the displacement P?

Picture

What am I missing?

Thanks.

 

[legoman666]

magnitude of what?

 

[Drako]

90cm, 180 degrees

 

[legoman666]

find the circumfrence. then use half the circumfrence (since it went half a revolution) to figure out how far the wheel traveled horizontally. use inverse sin, inverse cos or whatever (draw a pic to find out which one to use) to find the angle

 

[silverpig]

Originally posted by: Drako
90cm, 180 degrees

1/2 revolution...

 

[silverpig]

magnitude = sqrt[(45*Pi)^2 + 90^2]
Angle = arctan[2/Pi]


I probably messed something stupid up though.

 

[Drako]

Originally posted by: legoman666
find the circumfrence. then use half the circumfrence (since it went half a revolution) to figure out how far the wheel traveled horizontally. use inverse sin, inverse cos or whatever (draw a pic to find out which one to use) to find the angle

Yes, I was way over simplifying this.

The wheel rolled half the circumference which is 1/2 * (2*pi*r). So it rolled pi*r, and point P is at 2*r off the floor. You know two lengths of right triangle, so you should be able to figure out the rest .

 

[Drako]

Originally posted by: silverpig
magnitude = sqrt[(45*Pi)^2 + 90^2]
Angle = arctan[2/Pi]


I probably messed something stupid up though.

Looks correct to me!

 

[legoman666]

by my reckoning, 141.37cm displacement and P is at a 57.5 degree angle from where it was originally. pic: http://img209.imageshack.us/img209/6739/mathsoh5.gif

 

[Drako]

Originally posted by: legoman666
by my reckoning, 141.37cm displacement and P is at a 57.5 degree angle from where it was originally. pic: http://img209.imageshack.us/img209/6739/mathsoh5.gif

Nice picture, but the numbers are incorrect I believe.

167.75 cm
32.48 degrees

 

[CraKaJaX]

Thanks for the help guys. Cleared it up for me.

 

[CraKaJaX]

Originally posted by: Drako

Originally posted by: legoman666
by my reckoning, 141.37cm displacement and P is at a 57.5 degree angle from where it was originally. pic: http://img209.imageshack.us/img209/6739/mathsoh5.gif

Nice picture, but the numbers are incorrect I believe.

167.75 cm
32.48 degrees

Yea, that's also what I got.

 

[legoman666]

ah, used wrong inverse function. (i did arccos isntead of arcsin) and my 141.37cm was the horizontal dispalcement, not total displacement (but that is in the pic)