Acylinder with moment of inertia i about its center of mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling (figure 1) . the cylinder's vertical position as a function of time is y(t). at time t=0 the cylinder is released from rest at a height h above the ground.
a) the string constrains the rotational and translational motion of the cylinder. what is the relationship between the angular rotation rate ? and v, the velocity of the center of mass of the cylinder?
b) remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to positive angular velocity.
c) suppose that at a certain instant the velocity of the cylinder is v. what is its total kinetic energy, ktotal, at that instant?
d) suppose that at a certain instant the velocity of the cylinder is v. what is its total kinetic energy, ktotal, at that instant?