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(II) Calculate the net torque about the axle of the wheel shown in Fig. 8–42. Assume...

(II) Calculate the net torque about the axle of the wheel shown in Fig. 8–42. Assume that a friction torque of 0.60 m/N opposes the motion.

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Answer #1

The expression for magnitude of torque acting on an object about an axis of rotation is,

Here, is the length of radial line from the axis of rotation to the point of application of force, is the magnitude of force, and is the angle between the direction of force and the radial line from the axis of rotation to the point of application of force.

The below figure shows three forces acting at an angle of at a distance of from the rotation axis, acting at an angle of at a distance of from the rotation axis, and acting at an angle of at a distance of from the rotation axis.

Picture 1

Assume that the sign convention of clockwise torque to be negative and counterclockwise to be positive. In the given problem, all the forces are acting perpendicular to the axle. So, the angle between the direction of each force and the radial line from the axis of rotation to the point of application of force is equal to 90 degrees.

Calculate the torque due to the force of.

Substitute for, for, and for in the equation.

Calculate the torque due to the force of.

Substitute for, for, and for in the equation.

Calculate the torque due to the force of.

Substitute for, for, and for in the equation.

Express the frictional torque in terms of sign convention. As the frictional torque is opposing the motion, its direction is counterclockwise and its sign is taken as positive. Hence, the frictional torque is represented as,

Calculate the net torque about the axle of the wheel.

The net torque about the axle of the wheel is given by the algebraic sum of all the torques acting on the wheel.

Substitute for, for, for, and for.

The negative sign in the value of the net torque represents clockwise torque. Hence, the net torque about the axle of the wheel is equal to, which is acting in clockwise direction.

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