1

Rotor Torque

In this handout, we will briefly explore the concept of torque. Torque measures thetendency of an applied force to cause an object to rotate about a particular axis. Wecompute the torque, τ , as follows:

τ = r× F.

In the above equation, F (in N) is the force vector, r (in m) is the vector that points fromthe chosen axis to the point of application of the force. By definition, τ is a vector, andits direction and magnitude describe different aspects of the objects rotation.

Question 1 Suppose we use a 15 cm wrench and a force of 30 N to turn a nut counter-clockwise as seen in Figure 1a. Compute the torque τ resulting from this action.

Question 2 Suppose we use a 20 cm wrench and a force of 30 N to turn a nut counter-clockwise as seen in Figure 1a. Compute the torque τ resulting from this action.

Question 3 Suppose we use a 15 cm wrench and a force of 50 N to turn a nut counter-clockwise as seen in Figure 1a. Compute the torque τ resulting from this action.

Question 4 Suppose we use a 15 cm wrench and a force of 30 N to turn a nut clockwiseas seen in Figure 1c. Compute the torque τ resulting from this action.

(a) Counter-clockwise (b) Clockwise (c) Alternate

Figure 1: Different torque figures

Question 5 What does the magnitude of τ tell you about the rotation of the nut? (Hint:If you apply a larger force, would you expect the nut to turn slowly or quickly?)

Question 6 What does the direction of τ tell you about the rotation of the nut?

2

Question 7 What is the torque τ if F and r are parallel? Describe what is happening inthis situation.

The rotor of a helicopter exerts an equal, but opposite, rotational force on the bodyof a helicopter (Newton’s 3rd Law). If a helicopter’s rotors rotate counter-clockwise, thenthe body of the helicopter has a tendency to rotate clockwise (see Figure 2). This rotortorque must be counteracted in order to be able to fly the vehicle effectively.

Figure 2: Real caption1

A typical helicopter will have a tail rotor (see Figure 2) whose main purpose is tocounteract the problem of rotor torque. However, the Parrot drone does not seem to haveany kind of tail rotor (see Figure 3).

Figure 3: Parrot drone

Question 8 Examine the rotor blades of the Parrot drone. Are they all designed to turnin the same direction? Do some turn clockwise? counter-clockwise?

Question 9 Explain how the four rotors on the Parrot drone solve the problem of rotortorque.

Question 10 If the front left rotor suddenly stopped working, would the Parrot drone beginto turn clockwise or counter-clockwise?

1http://www.flightsimbooks.com/gunship/image030-1.jpg