September 12th, 2012, 01:22 AM  #1 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Centre of mass
I need some help with this problem. A uniform disc is projected down a plane that has incline at angle a to the horizontal. The unit vector i points down the line of greast slope of the plane and the unit vector j is perpendicular. The coefficient of frictin between the disc and the plane is 2 tan a. I have the forces acting on the disc as F = F i N = N j W = Mg sin a i MG cos a j If the centre of the disc has moved a distance x down the slope at time t, I need to determine the equation of motion of the centre of mass of the disc. So far I have Newtons 2nd Law: Mx(double dot)i= N+F+W Resolving in the idirection Mx=F+Mg sin a but F = 2 tan a Resolving in the jdirection NMg cos a = 0 therefore N=Mg cos a Mx = 2 tan z + Mg cos a  Mg sin a x= 2 tan + g cos a  g sin x I need to show this becomes x= g sin a can anyone help? 
September 12th, 2012, 03:31 AM  #2 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Centre of mass
Actually, I get f = 2 tan a Hence Mx =  2 tan a + Mg cos a + Mg sin a x=  2 tan a + g cos a + g sin a x = 2 g sin a + g sin a x =  g sin a Does this look right? 
September 12th, 2012, 08:49 AM  #3 
Newbie Joined: May 2012 Posts: 3 Thanks: 0  Re: Centre of mass
I'd suggest reading the question again


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