# Torque of cyclinder

I really need help with the following problem.

1) A 2kg mass is attached to a string which is wrapped several times around a uniform solid cyclinder of radius 3m and moment of inertia of I = 5kg m/s^2. Assume: The cyclinder can rotate freely. The acceleration of gravity is 9.8m/s. Find the torque on the cyclinder. Answer in units of N.m

## Answers and Replies

F x L = T
F (Force) is the force of gravity pulling on the 2kg mass, which converts to 19.6N.
L (Length) is the distance to the focal point which is 3m (the radius of the cylinder).

Moment of inertia is not used in this problem.

NateTG
Science Advisor
Homework Helper
Pergatory said:
Moment of inertia is not used in this problem.

Since the acceleration of the cylinder downward affects the torque, moment of inertia is important, but isn't moment of intertia supposed to be in units of $$kg m^2$$?

ke2cool:
List the forces that are acting on the cylinder.
List the net torque on the cylinder in terms of those forces.
See what equations apply to the situation.

OT: Any idea what that cylinder is made of? A 6m diameter and it only weighs 2kg.

I think Nate's jumped off the deep end... cookiemonster

Doc Al
Mentor
find the tension in the string

ke2cool said:
1) A 2kg mass is attached to a string which is wrapped several times around a uniform solid cyclinder of radius 3m and moment of inertia of I = 5kg m/s^2. Assume: The cyclinder can rotate freely. The acceleration of gravity is 9.8m/s. Find the torque on the cyclinder. Answer in units of N.m
I presume that the cylinder rotates about a fixed horizontal axis? And that you just messed up the units of I? (As NateTG pointed out.)

The only force exerting a torque on the cylinder is the tension in the string.

Identify all the forces acting on the mass and all the forces acting on the cylinder. Then apply Newton's 2nd law to both objects to get two equations so you can solve for the tension.

Hint: You'll have to relate the angular acceleration of the cylinder to the linear acceleration of the mass.