Question

angular displacement of a point moving in a circle of 10cm.when displacement of projection of this point along vertical diameter of circle is 8.66cm will be

Answer 1

The angular displacement is 60°.

A body starting at point A, reaches a point B in a time t. In this time, the foot of the perpendicular drawn from the point on to the vertical diameter, makes a displacement from O to C. The angular displacement is the angle θ  swept out by the radius vector of magnitude R. This is shown in the diagram attached.

In triangle OBC, ∠OBC is equal to θ .

From the ΔOBC,

$sin\theta= \frac{y}{R}$

Substitute 10 cm for R and 8.66 cm for y.

$sin\theta= \frac{y}{R} =\frac{8.66 cm}{10 cm}  =0.866\\  \theta = sin^-^1(0.866)=60^o$

The angular displacement is 60°.