An object is spun around in circular motion such that its frequency is 12 Hz. a. What is the period of its rotation?
b. How much time will be required to complete 86 rotations?

The period of rotation is 1/12 seconds and it takes 7.17 seconds to complete 86 rotations.

Time period (T) in a rotational or periodic motion is defined as the time taken to complete one rotation and frequency (f) is the reciprocal of time period.

                         f = 1/T   ⇒  T = 1/f  , given  that f = 12 Hz

                          T = 1/12 s is the time period of ne rotation

Now if time takes to complete one rotation is 1/12s , then to complete 86 rotation, the time required is

                               t = 86×(1/12) = 7.17 seconds is taken to complete 86 rotations.

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Explanation:

Given parameters:

Frequency  = 12Hz

Unknown:

a. Period of its rotation

b. Time required to complete 86 rotations

Solution:

Frequency is the number of times of rotation per unit of time.

  Frequency  =  

Period is the opposite of frequency;

          Period =   = 0.083s

b. Time for 86 rotations;

          Since frequency  =  

n is the number of rotation

t is the time

             t  =  =   = 7.2s

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