A cross-section of a solid cylinder is shown in Fig. 7.2.20, with the core section protruding from the larger drum. A rope wrapped around the drum of radius `r_(1) = 80` cm exerts a force 10.0 N to the right on the cylinder. The cylinder can rotate freely around the central axis. A rope wrapped around the core of radius `r_2 = 40 cm` exerts a force of 15.0 N downwards on the cylinder, (a) Calculate the net torque acting on the cylinder about the axis of rotation ?

Explanation

Radius of the drum `=r_(1) = 0.80 m`
Radius of the core = `r_(2) = 0.04 m`
Force acting on the drum `=F_(1) = 10.0 N`
Force acting on the core `=F_(2) = 15.0 N`
The axis of rotation passes through the centre of the core and perpendicular to the plane of the core. The torque due to `F_(1)` is `-r_(1)F_(1)` as it produces a clockwise rotation and the torque due to `F_2` is `r_2 F_2` as it produces and anticlockwise rotation. Net torque is `sigma_("net") = tau_(1)+ tau_(2)`
`=0.4 xx 15 -0.8 xx 10`
`=-2.0 Nm`
The net torque is negative and so the cylinder rotates in the clockwise direction.