A solid cylinder of mass m and radius r lies flat on a frictionless horizontal t

Question

A solid cylinder of mass m and radius r lies flat on a frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The circumference of the cylinder is sufficiently rough so that the string does not slip with respect to it. What is the acceleration of the mass m attached to the end of the string? Please solve using torques and angular momentum

A solid cylinder of mass m and radius r lies flat on a frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The circumference of the cylinder is sufficiently rough so that the string does not slip with respect to it. What is the acceleration of the mass m attached to the end of the string? Please solve using torques and angular momentum

Explanation / Answer

so torques about cylinder where F is the force on the other side of the rope
rT - rF = I

if no slipping =a/r and we know I = 1/2 mr^2

rT - rF = 1/2 m r^2 (a/r)

T - F = 1/2 m a

for the mass

F = ma

plug into other equation

T - ma = 1/2 ma

T = 3/2 m a

a = 2 T/(3m)

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