3. Angle of Twist and Torsional Deformation

Try these first

1. 1.

   What does the angle of twist represent?

   Hint

   Think about what happens to a shaft when you apply a force to it.

2. 2.

   What is the formula for angle of twist?

   Hint

   Remember the acronym TL-G-J!

3. 3.

   What is the angle of twist formula?

   • θ = TL/GJ
   • θ = T/GJ
   • θ = TL^2/G

   Hint

   Look for the equation that includes torque and length in the numerator.

4. 4.

   True or False: The angle of twist increases with the length of the shaft.

   • True
   • False

   Hint

   Consider what happens as more material is added.

5. 5.

   A steel shaft with a diameter of 0.05 m and length of 2 m has a shear modulus of 80 GPa. If a torque of 150 Nm is applied, calculate the angle of twist and discuss how changing the diameter affects the outcome.

   Hint

   Remember to deal with unit conversions if necessary.

6. 6.

   Design a system with a hollow shaft that connects two gears. If the outer diameter is 0.1 m and the inner diameter is 0.06 m with a length of 1.5 m, how would you determine the required torque if the desired angle of twist is limited to 0.02 radians?

   Hint

   Start by finding J for the hollow shaft.