In Exercises answer the given questions about the indicated examples of this section.

In Example 1, what is the equation relating d and t if the end of the radius starts at (0, R)?

Data from Example 1

In Fig. 10.33, assume that a particle starts at the end of the radius at (R, 0) and moves counterclockwise around the circle with constant angular velocity ω. The displacement of the
projection on the y-axis is d and is given by d = R sinθ. The displacement is shown for a few different positions of the end of the radius. Because θ/t = ω, or θ = ωt, we have d = R sinωt

as the equation for the displacement of this projection, with time t as the independent variable. For the case where R = 10.0 in. and ω = 4.00 rad/s, we have d = 10.0 sin 4.00t

By sketching or viewing the graph of this function, we can find the displacement d of the projection for a given time t. The graph is shown in Fig. 10.34.

y (in.) 10 -10 V 1 2 2 Fig. 10.34 3 T t (s)