19.5 : ねじれ角 – 問題解決

The electric motor exerts a 700 N-m torque on an aluminium shaft, causing it to rotate at a constant speed. Pulleys B and C experience torques of 300 N-m and 400 N-m, respectively. The modulus of rigidity is given as 25 GPa. If the length and diameter of each section are known, calculate the angle of twist between the pulleys B and C.

First, a cut is made between pulleys B and C, and a free-body diagram of the cut cross-section is considered.

The torque acting on the pulley B is anticlockwise. So, using the principle of equilibrium, the torque at the cut cross-section of the shaft will be equal and opposite to the torque at pulley B.

Next, the polar moment of inertia at the cut cross-section, which is proportional to the fourth power of the radius of the shaft, is calculated.

By substituting all the known parameters, the angle of twist between pulleys B and C is determined. The angle obtained is in radians and can be converted to degrees.