a uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity w about a vertical axis passing through one end. the tension in the rod at a distance x from the axis is?
Answers
Answered by
17
AB is a rod of length l ,mass M & this rod is rotating about end A....
now , mark a point c anywhere on the rod , distance bw end A & C is x ...
now the rod is divided into two parts , AC & CB .......
tension of rod at point C is (T)= dmw2r (dm is mass of part BC = m(l-x)/l )
=M(l-x)w2r/l
this r is the distance of center of mass of BC from end A so r = (x+l)/2
so
T = M(l-x)(l+x))w2 /2l
T = M(l2-x2)w2 /2l
this is the expression for tension at any point
now , mark a point c anywhere on the rod , distance bw end A & C is x ...
now the rod is divided into two parts , AC & CB .......
tension of rod at point C is (T)= dmw2r (dm is mass of part BC = m(l-x)/l )
=M(l-x)w2r/l
this r is the distance of center of mass of BC from end A so r = (x+l)/2
so
T = M(l-x)(l+x))w2 /2l
T = M(l2-x2)w2 /2l
this is the expression for tension at any point
Answered by
12
T=mw²(l²-x²)/2 ... Tension
Similar questions
Math,
7 months ago