Another Physics Problem

[Sidoh]

I think that this is a bit more difficult than the last one I posted!  I hope so, at least.  In any case, here it is...

Center of Percussion

A baseball bat rests on a frictionless, horizontal surface. The bat has a length of 0.900 m, a mass of 0.800 kg, and its center of mass is 0.600 m from the handle end of the bat. The moment of inertia of the bat about its center of mass is . The bat is struck by a baseball traveling perpendicular to the bat. The impact applies an impulse at a point a distance x from the handle end of the bat. The point on the bat you have located is called the center of percussion. Hitting a pitched ball at the center of percussion of the bat minimizes the "sting" the batter experiences on the hands.

Edit -- I got so caught up with making sure the format was correct that I forgot the rest of the question!  Sorry.

What must x be be so that the handle end of the bat remains at rest as the bat begins to move? (Hint: Consider the motion of the center of mass and the rotation about the center of mass. Find  so that these two motions combine to give for the end of the bat just after the collision.  Also, note that the integration of equation gives )

[Sidoh]

I solved this one.  If anyone is interested in the solution, I can post it.

Here's another difficult one...

The moment of inertia of the front wheel of a bicycle about its axle is 8.40*10^-2 kg*m^2 , its radius is 0.390 m, and the forward speed of the bicycle is 5.90 m/s.

With what angular velocity must the front wheel be turned about a vertical axis to counteract the capsizing torque due to a mass 54.0 kg  located a distance 4.00×10^-2 m horizontally to the right or left of the line of contact of wheels and ground?

Here's some of the equations for angular motion:

[Explicit]

Sidoh, why come Explicit no can read equations? 

But yeah, I can't see it for some reason.

[Sidoh]

Sidoh, why come Explicit no can read equations? 

But yeah, I can't see it for some reason.

It's hosted on my home connection, so it could simply be the slow transfer speed.  It took a while for it to load for me as well.  I may try attempting to install the same rendering engine on my account here at school, but I sort of doubt they have ImageMagik installed on them, which is required for the script to work.

Can you access www.sidoh.org with any luck?

Edit: Hmm, it doesn't seem to be the connection.  I can move around fine in SSH.  Normally, when the bandwidth is being strangled (usually my sister downloading something), it becomes extremely painful to use SSH.  I guess the thing is just behaving poorly.  If it doesn't shape up, I'll reboot it.  I need to rebuild the thing sometime soon... maybe over Christmas break.

In any case, here's the first problem in PDF form.

Here's the second in a PDF as well.