A cylinder of mass M and radius 2R (careful!) is at rest on a rough table. A light string runs from the center of the cylinder in such a way as to allow the cylinder to be pulled horizontally. Said string runs over a disc of mass m and radius R on a frictionless axle. The string continues down over the disc and is connected to a hanging mass M. Once released from rest, the cylinder rolls without slipping on the table, and the string does not slip over the disc. What is the linear acceleration of the masses? HINT: You can NOT assume that Ffs = μfsFN
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
A cylinder of mass M and radius 2R (careful!) is at rest on
a rough table. A light string runs from the center of the
cylinder in such a way as to allow the cylinder to be
pulled horizontally. Said string runs over a disc of mass
m and radius R on a frictionless axle. The string
continues down over the disc and is connected to a
hanging mass M.
Once released from rest, the cylinder rolls without
slipping on the table, and the string does not slip over the disc. What is the linear acceleration
of the masses?
HINT: You can NOT assume that Ffs = μfsFN here. The frictional force is just enough to prevent
slipping of the surfaces. You can NOT assume that the tensions are the same in each part of the
string
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