Rotational motion begining with kinetic friction.

[MarkChoo]

Homework Statement

A ball is suddenly kicked across a floor. It initial will have a linear velocity, but no initial angular velocity. The object will slide for a distance "d" until perfect rolling kicks in.

all are in terms of variables and not specific numbers

A.) derive an equation for linear acceleration of center of mass.
B.) deriave an equation for angular acceleration.
C.) Find final speed of the ball when pure rolling beings in terms of Vo
D.) determine the time and distance that the ball slid.

Homework Equations

I=2/5mR^2
Torque=(I)(alpha)
alpha = a/R
mgr?
wf = 2(alpha)(theta) + wi

The Attempt at a Solution

A.) T=I(alpha)
mgur = I(alpha)
mgur = I(a/R)
a= 5gu/2?

B.) alpha = u5g/2r?

very lost with the rest.

 

[alphysicist]

Hi MarkChoo,

Homework Statement

A ball is suddenly kicked across a floor. It initial will have a linear velocity, but no initial angular velocity. The object will slide for a distance "d" until perfect rolling kicks in.

all are in terms of variables and not specific numbers

A.) derive an equation for linear acceleration of center of mass.
B.) deriave an equation for angular acceleration.
C.) Find final speed of the ball when pure rolling beings in terms of Vo
D.) determine the time and distance that the ball slid.

Homework Equations

I=2/5mR^2
Torque=(I)(alpha)
alpha = a/R
mgr?
wf = 2(alpha)(theta) + wi

The Attempt at a Solution

A.) T=I(alpha)
mgur = I(alpha)
mgur = I(a/R)

This last step is not true; since the ball has not started pure rolling yet (it is sliding as it rolls), then alpha is not equal to a/R.

Instead of using torque, draw a force diagram and use Newton's law.

a= 5gu/2?

B.) alpha = u5g/2r?

That looks right to me.

 

[MarkChoo]

im lost then how to get the linear acceleration, because that was the only way I saw how to get alpha(a rad/s^2 value) in terms of a m/s^2 value. If that's what they mean by linear.

 

[alphysicist]

im lost then how to get the linear acceleration, because that was the only way I saw how to get alpha(a rad/s^2 value) in terms of a m/s^2 value. If that's what they mean by linear.

You get it the same way that you find the acceleration in simpler (non-rotational) problems. Draw a force diagram for the ball with all forces acting on it. Then use Newton's law (F_net=ma) in the horizontal and vertical directions to get two equations; by putting them together you can find the acceleration.

 

[MarkChoo]

how about if i use Wf=alpha(t) + Wo and plug into my alpha to get...
t= 2rWf/5gu

then plug time t it into Vf= at + Vo
then I solve for a?

 

[alphysicist]

how about if i use Wf=alpha(t) + Wo and plug into my alpha to get...
t= 2rWf/5gu

then plug time t it into Vf= at + Vo
then I solve for a?

I don't believe that will give you what you want by itself; you'll end up with an expression that contains either the final angular velocity or final linear velocity, which is what the problem later wants you to find (in part c).

Have you tried to use a force diagram to find the linear acceleration, as I mentioned in my last post? What does that give you?

 

[MarkChoo]

yea I've tried a force diagram.

ive also tried F = ma and since Ff = n u

nu=ma

then

a = nu/m

 

[alphysicist]

yea I've tried a force diagram.

ive also tried F = ma and since Ff = n u

nu=ma

then

a = nu/m

Exactly; that's what the horizontal equation of the force diagram gives you.

Now just write an expression for the vertical forces, and that will tell you what n is in your equation. There are two vertical forces here; how are they related to each other?