# Precession

##### Demonstration

To show how the spin axis of the Earth rotates or precesses.

Large gyroscope

Eye protection

#### Health & Safety and Technical notes

1 A suitable gyroscope is available from ASCOL.

Alternatively, a gyroscope can be made from a bicycle wheel; a front wheel, 46 cm x 3 cm is satisfactory. Two 10 cm lengths of alkathene rod (or similar) can be used for handles. Drill out the two lengths of plastic rod axially to a depth of 2.5 cm with a 6 mm drill. Screw them firmly on to the axle of the wheel to provide the two handles. Wear eye protection when drilling. The bicycle wheel is even better if it is loaded with a tyre of lead strip. Make sure the lead is firmly fixed to the wheel.

2 Drill a 3 mm hole through a diameter of one of the handles about 1 cm from the end. Pass a knotted string through this hole.

3 If the large gyroscope is not available, a toy gyroscope could be used.

#### Procedure

a Hold the wheel vertically in one hand and set it rotating - a series of tangential swipes with the palm of the other hand will do, or spin it rapidly by holding the rim against a motor-driven wheel. Be careful that clothing does not become entangled in the rotating motor.

b When the wheel is rotating rapidly it can be supported by the string. It will remain vertical and will precess.

#### Teaching notes

1 The wheel spinning rapidly represents the spinning Earth and the massive rim of the wheel represents the equatorial bulge.

2 Precession is the slow, conical motion of the Earth’s spin-axis round the axis of the ecliptic; that is, around a line through the Sun perpendicular to the Earth’s orbit, an axis at 23.5o from the Earth’s polar axis.

3 Newton showed that this motion is a consequence of gravitation and the Earth’s spin. A spherical Earth, whether spinning or not, would keep its axis pointing in a constant direction among the stars as it followed its orbit around the Sun.

4 An Earth with an equatorial bulge will suffer extra gravitational pulls exerted by the Sun (and Moon) on the bulge. These extra forces applied to a spinning body show that rocking forces applied to a spinning body do not succeed in rocking the body, but produce precession instead.

5 The Earth, a spinning top, and a ‘mysterious gyroscope’ all precess in the same way, for the same reason. In the sketches above ‘torque axis’ means the axis around which the tilting force tries to rock the spinning object.

6 Crude explanation with Newton’s Law II, considering only the top and bottom of rim, A and B. If wheel rocks ever so little in response to torque, A gains momentum Δmv to the right; B gains Δmv to the left. Combining these with previous momenta, we find wheel must be precessing.