My current algebra class is using Fraleigh's "First Course in Abstract Algebra", and it doesn't feel very challenging (and is extremely verbose!). I'd like to study the subject deeper, since I really enjoy it. I picked up Lang's "Undergraduate Algebra", which seems to be much better, but if...
The condition states that the cart is rolling, which I suppose means that it's rolling without slipping. The condition for rolling without slipping is:
v=R\omega
I can't see the picture, but what you generally do in problems like this is break apart the rod into small pieces (dL), find the contribution of one piece to the force (dF), and then integrate. The mass of this small piece will be (M/L)dl, since M/L is the linear density (I'm assuming that the...