I tried to solve a physics problem that involves a cylinder on a truck that is accelerating. I'm supposed to solve the acceleration of the center of mass of the cylinder when the acceleration of the truck, and the radius and the mass of the cylinder are known. The cylinder rolls without slipping.
In the solution it is said that as the rolling occurs without slipping, the point on the cylinder that is in contact with the truck accelerates at the same rate as the truck. Why is this true? I can understand that their speed should be the same as they are momentarily in contact, but why their accelerations?
I've been taught that if an object is under forces, regardless of the positions of the forces wrt. the center of mass, the acceleration of the COM is the sum of these forces. So if one point on the cylinder accelerates at the same rate as the truck, why doesn't the COM of the cylinder accelerate also at the same rate as the truck?