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Question

1) An object is spun around in a circle of radius 3.0 m with a period of 1.5 s. What is the magnitude

of the velocity?

2) An object is spun in a circle of radius 1.2 m with a frequency of 10.0 Hz. What is its velocity?

Answer 1

The period tells us how long it takes an object to complete a cycle, or in this case, a revolution (since it's circular motion). Since the period is 1.5 seconds, it takes 1.5 seconds to make one revolution.

The distance that an object travels in a circle is equal to the circumference of that circle, which is given by the formula:

C = 2πr

So in one revolution, the distance traveled is

C = 2πr

C = 2π*3

C = 6π

C ≅ 18.85 m

Since it takes 1.5 seconds to travel 18.85 m, the velocity is

v = Δx/t

v = 18.85/1.5

v = 12.57 m/s

2) In problem 2, you're given the frequency. The frequency is the inverse of the period, or

f = ¹/_T

So

T = ¹/_f

T = ¹/₁₀

T = 0.1 sec

You can use the same method in part 1 for part 2 now

V = ^2πr/_T

V = ^2*π*1.2/_0.1

V = 75.4 m/s