For particle P revolving about centre O in a circle of radius r with angular velocity ω, as shown in the figure, the projection of OP on the x-axis at time t is:

Question

G1 Physics · Accepted Answer

The projection of uniform circular motion on a diameter is simple harmonic motion. From the figure, the radius OP initially makes an angle φ = π/6 with the positive x-axis. After time t, the angular position is θ = ωt + π/6 The x-coordinate is therefore x(t) = r cosθ = r cos(ωt + π/6) Hence option A follows.