Question

In latitude 25.0 S, SA (spin axis) of a FG (free gyro) is in position S40E and horizontal. Find the tilt after 6 hours.

(a) 61.16 up

(b) 61.16 down

(c) 51.15 up

(d) none of the mentioned

I got this question in quiz.

The origin of the question is Effect of Gyroscopic Couple on a Naval Ship during Steering and Pitching in portion Gyroscopic Couple and Precessional Motion of Machine Dynamics

Answer 1

Right choice is (a) 61.16 up

For explanation: PZ= 65, ZX = 90, tilt after 6 hours = 90 – ZY =?

In triangle PZX,

Cos PX = Cos Z Sin PZ

Cos PX = Cos 40 Sin 65

Cos PX = 0.694272

PX = PY = 46.031

Again, in triangle PZX,

Cos P = – Cot PZ Cot PX

Cos P = – Cot 65 Cot 46.031

P or angle ZPX = 116.732

Angle XPY = 6 hours = 90. Thus, angle ZPY = 26.732

In triangle PZY,

Cos ZY = Cos P Sin PZ Sin PY + Cos PZ Cos PY

Cos ZY = Cos 26.732 Sin 65 Sin 46.031 + Cos 65 Cos 46.031

ZY = 28.839 and tilt = 61.16 up.