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A gyroscope is processing about a vertical axis. What happens to the precession angular speed if the following changes are made, with all other variables remaining the same?

(a) The angular speed of the spinning flywheel is doubled;

(b) The total weight is doubled;

(c) The moment of inertia about the axis of the spinning wheel is doubled;

(d) The distance from the pivot to the center of gravity is doubled.

(e) What happens if all the variables in parts (a) through (d) are doubled?

In each case justify your answer.

Short Answer

Expert verified

(a) The precession angular speed will be cut in half.

(b) The precession angular speed doubles.

(c) The precession angular speed will be cut in half.

(d) The precession angular speed doubles.

(e) The precession angular speed stays the same.

Step by step solution

01

Formula used

Precession angular speed is

Ω=wrlwwhere,

w is the weight of the flywheel

r is the distance from the pivot to the center of gravity

I is moment of inertia and

Ó¬angular speed.

02

(a)Step 2: Angular speed is doubled

From the formula, it is clear that precession angular speedΩis inversely proportional to the angular speed Ӭ.

So if Ӭis doubled, Ωwill be halved.

Hence, precession angular speedΩwill be cut in half.

03

(b)Step 3: total weight is doubled

From the formula, it is clear that precession angular speed Ω is directly proportional to weight w.

So if w is doubledΩ, will also be doubled l.

Hence, precession angular speedΩwill be doubled.

04

(c)Step 4: Moment of inertia is doubled

From the formula, it is clear that precession angular speed Ω is inversely proportional to the moment of inertia I.

So if I is doubled Ω, will be halved.

Hence, precession angular speedΩ will be cut in half.

05

(d)Step 5: Distance from the pivot to the centre of gravity is doubled

From the formula, it is clear that precession angular speedΩ is directly proportional to the distance from the pivot to the centre of gravity r.

So if r is doubled,Ω will also be doubled.

Hence, precession angular speedΩ will be doubled.

06

(e)Step 6: All variables are doubled

If all four factors are doubled, the total effect will be balanced and precession angular speedΩ remains the same.

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