Question

Визначити період та частоту обертання тіла якщо за 3 хв воно здійснило 600 обертів.

Answer 1

Calculating Period and Frequency of Rotation

To determine the period and frequency of rotation of the body, we can use the following formulas:

Period (T) is the time taken for one complete rotation. Frequency (f) is the number of rotations per unit time.

Given that the body completed 600 rotations in 3 minutes, we can calculate the period and frequency using the following steps:

1. Calculate Period (T): - The period can be calculated using the formula: \[ T = \frac{t}{n} \] where \( t \) is the total time and \( n \) is the number of rotations.

- Substituting the given values: \[ T = \frac{3 \text{ min}}{600} \]

This gives us the period of rotation.

2. Calculate Frequency (f): - The frequency can be calculated using the formula: \[ f = \frac{1}{T} \] where \( T \) is the period.

- Substituting the calculated period value: \[ f = \frac{1}{T} \]

Let's calculate the period and frequency using the given data.

\[ T = \frac{3 \text{ min}}{600} \]

\[ f = \frac{1}{T} \]

Calculation

\[ T = \frac{3 \text{ min}}{600} = 0.005 \text{ min/rotation} \]

\[ f = \frac{1}{T} = \frac{1}{0.005} = 200 \text{ rotations/min} \]

So, the period of rotation is 0.005 minutes/rotation and the frequency of rotation is 200 rotations per minute.

These calculations are based on the given data and the formulas for period and frequency of rotation. [[1 #]], [[2 #]], [[3 #]]