Barron's 2nd Edition DT Q28

Barron's Book

28) We are given a situation about an object in circular motion. We are asked to find the speed of the object. Many people gravitate towards using the centripetal force to solve this problem. But it is important to recognize that using centripetal force will not help us solve the equation.

Where F[c] is centripetal force, m is mass, v is speed, r is radius of path, and a is acceleration

In this equation, we would have two unknowns, so instead, we should use a different method.

---

Let's try just using the general definition of speed.

Where v is speed, d is distance, and t is time

For 1 revolution, the object travels around the circumference of the circle. So we can use the circumference of the circle as the distance(d). Additionally, since it is one revolution, we can use the period(T) for our time(t).

Where v is speed, d is distance, t is time, r is radius, and T is period

We are already given the radius, but we don't know the period. However, we are given the frequency. Since frequency is the reciprocal of the period, we can quickly find the period and plug in our values to solve for the speed.

Where v is speed, r is radius, T is period, and f is frequency

Answer: C