Question

Problem 5: Torque 

A one-piece cylinder is shaped as shown in the figure, with a core section protruding from the larger drum. The inner cylinder has a mass of 3 kg and the outer cylinder has a mass of 8 kg. The cylinder is free to rotate about the central axis shown in the drawing A rope wrapped around the drum, which has radius R1 = 0.3 m, exerts a force T₁ = 50 N to the right on the cylinder. A rope wrapped around the core, which has radius Rp = 0.1 m, exerts a force T2 = 25 N downward on the cylinder. The moment of inertia of a uniform solidcylinder is I = 1/2MR² .

a) What is the net torque on the cylinder? 

b) What is the angular acceleration of the cylinder?  

Answer 1

Calculte the net torque Tnet

Tnet = R1T1 - R2T2

Here R is radius of cylinder and T is tension applied.

Tnet = 0.3 m * ( 50 N) - ( 0.1 m ) (25 N)

Tnet = 12.5  N-m clockwise

(b)

Net mass moment of inertia Inet

Inet = 0.5 [ ( 3 kg *0.3^2 + 8 kg *0.1^2 )]

Inet = 0.175 kg -m^2

We know angular acceleration and torque relationship.

Tnet = Inet * alfa

Angular acceleration (alfa) = 12.5 / 0.175

Alfa = 71.42 rad/s^2 (answer).