- #1
monsterdivot
- 4
- 0
Hi All,
I'm trying to figure out how to model a rolling ball in the x y plane.
I've started with the basic equation of motion with constant acceleration
d = v[tex]_{}0[/tex]t + 1/2at[tex]^{}2[/tex]
v[tex]_{}0[/tex] is the initial velocity
a is acceleration
t is time
Assume that v is a vector at an angle [tex]\alpha[/tex] with the x axis.
If the plane is flat, a is is all due to the force of rolling resistance F[tex]_{}r[/tex]. I represent F[tex]_{}r[/tex] as a vector in the opposite direction to v. Is this the correct way to treat rolling resistance? If so, does this mean that if we decompose the equation into x and y components, does this mean that F[tex]_{}r[/tex] should be decomposed into x and y components?
F[tex]_{}rx[/tex] = F[tex]_{}r[/tex]sin[tex]\alpha[/tex]
and
F[tex]_{}ry[/tex] = F[tex]_{}r[/tex]cos[tex]\alpha[/tex]
Given that I'm treating F as a vector it makes sense to do this, but it doesn't feel right to me. This means that the rolling resistance varies in x and y with the angle of the vector v.
Is this right? Also, is F independent of the speed of the ball?
Sorry about the appearance. The subscripts aren't working for some reason. Only the t squared should show as a superscript. the rest should be subscripts.
Thanks for any help you can give.
I'm trying to figure out how to model a rolling ball in the x y plane.
I've started with the basic equation of motion with constant acceleration
d = v[tex]_{}0[/tex]t + 1/2at[tex]^{}2[/tex]
v[tex]_{}0[/tex] is the initial velocity
a is acceleration
t is time
Assume that v is a vector at an angle [tex]\alpha[/tex] with the x axis.
If the plane is flat, a is is all due to the force of rolling resistance F[tex]_{}r[/tex]. I represent F[tex]_{}r[/tex] as a vector in the opposite direction to v. Is this the correct way to treat rolling resistance? If so, does this mean that if we decompose the equation into x and y components, does this mean that F[tex]_{}r[/tex] should be decomposed into x and y components?
F[tex]_{}rx[/tex] = F[tex]_{}r[/tex]sin[tex]\alpha[/tex]
and
F[tex]_{}ry[/tex] = F[tex]_{}r[/tex]cos[tex]\alpha[/tex]
Given that I'm treating F as a vector it makes sense to do this, but it doesn't feel right to me. This means that the rolling resistance varies in x and y with the angle of the vector v.
Is this right? Also, is F independent of the speed of the ball?
Sorry about the appearance. The subscripts aren't working for some reason. Only the t squared should show as a superscript. the rest should be subscripts.
Thanks for any help you can give.
Last edited: