Text 2a. Vectors and Scalars

Read the text and define the following terms

vector; spin vector; scalar torque vector.

In order to answer this question, let us start with vectors. As you recall, a vector represents a physical quantity which has both magnitude (how much) and direction (which way). For example, the vector velocity has both magnitude (say 50 mi/hr) and direction (say North). By comparison, scalar quantity has only magnitude. Speed is a scalar quantity which has a magnitude (mi/hr) but does not have an associated direction.

Two factors are helpful in explaining the action of a gyro. First, there is the spin vector. The spin vector, an angular velocity, describes the way in which the gyro rotor rotates. The magnitude of the spin vector is measured in rad/sec, deg/sec, rev/min, etc.

The direction of the spin vector is found by wrapping the fingers of the right hand in the direction of spin rotation. Now, if the thumb assumes the usual hitch-hiking position, it points in the direction of the spin vector.

Consider the case where the spin motor is rotating counterclockwise when viewed from above. Wrapping the fingers of the right hand around the gyro in the direction of the spin, the thumb points up. Therefore, the spin vector points up. On the other hand, if the spin motor were rotating clockwise when viewed from above, the spin vector would point down.

THE RIGHT HAND SCREW RULE

This method of determining vector direction is known as the right hand screw rule. Imagine a wooden screw with a right hand thread—that is, where the thread spirals to the right from head to tip when viewed from the head end. The vector direction is the direction the screw would advance if the head were rotated in a clockwise direction when viewed from the head end.

Second, there is the torque vector. Torque is a force which tends to produce rotation or twisting. The magnitude of the torque is measured in dyne-centimeters, ounce-inches, pound-feet, etc. The amount of torque is found by multiplying the amount of force times the length which is the shortest distance between the force and what would be the axis of rotation. This shortest distance is called the moment arm. Assume that the force is 20 lbs and the moment arm is 4 ft long. Then the torque being exerted is 20 lbs 4 ft 80 lb-ft or

F* L =T

Where F= force, L= moment arm, and T= torque.

Torque being exerted= length.