## Essential University Physics: Volume 1 (3rd Edition)

a) We know the following equation for a position on a circle: $cos\theta \hat{i} +sin\theta \hat{j}$ To specify for a specific circle, we multiply by the radius, giving: $\vec{r}=R(cos\theta \hat{i} +sin\theta \hat{j})$ b) We know that the percentage of the cycle it will have completed at any point is equal to $\frac{t}{T}$. Multiplying this by 360, we find that the value of theta, in degrees, is: $\theta = \frac{360t}{T}$ c) The second derivative is: $=R(-cos\theta \hat{i} -sin\theta \hat{j})$ Based on the negatives, we see that the direction is toward the center of the circle. In addition, we know that the magnitude of an acceleration vector is $\frac{v^2}{R}$.