Rotational motion begining with kinetic friction.

In summary, the conversation discusses a problem involving a ball being kicked across a floor with initial linear velocity and no initial angular velocity. The ball slides for a distance "d" until it begins pure rolling. The conversation then asks to derive equations for linear and angular acceleration, find the final speed of the ball when pure rolling begins, and determine the time and distance the ball slid. The relevant equations used are I=2/5mR^2, Torque=(I)(alpha), alpha = a/R, mgr?, and wf = 2(alpha)(theta) + wi. The solution involves finding the linear acceleration using a force diagram and Newton's law, and then using the relationship between vertical forces to solve for n in the equation a
  • #1
MarkChoo
8
0

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.
 
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  • #2
Hi MarkChoo,

MarkChoo said:

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.
 
  • #3
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.
 
  • #4
MarkChoo said:
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 (Fnet=ma) in the horizontal and vertical directions to get two equations; by putting them together you can find the acceleration.
 
  • #5
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?
 
  • #6
MarkChoo said:
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?
 
  • #7
yea I've tried a force diagram.

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

nu=ma

then

a = nu/m
 
  • #8
MarkChoo said:
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?
 

1. What is rotational motion?

Rotational motion refers to the movement of an object around an axis or pivot point. This type of motion is commonly seen in circular or spinning objects, such as a wheel or a top.

2. What is kinetic friction?

Kinetic friction is the force that acts between two surfaces when they are in motion relative to each other. It is caused by the irregularities and bumps on the surfaces, which create resistance and slow down the movement.

3. How does kinetic friction affect rotational motion?

Kinetic friction can cause rotational motion to slow down or come to a stop. This is because the frictional force acts in the opposite direction of the object's movement, creating a torque or rotational force that opposes its motion.

4. What factors affect the amount of kinetic friction in rotational motion?

The amount of kinetic friction in rotational motion is affected by the types of surfaces in contact, the force pressing the surfaces together, and the speed of the rotation. Rougher surfaces, greater force, and higher speeds typically result in higher levels of kinetic friction.

5. How can we reduce the effects of kinetic friction in rotational motion?

One way to reduce the effects of kinetic friction in rotational motion is by using lubricants, such as oil or grease, between the two surfaces. This helps to fill in the gaps and smooth out the surfaces, reducing the resistance and allowing for smoother rotational motion. Another way is to use ball bearings, which also help to reduce friction by allowing the surfaces to roll instead of slide against each other.

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