Question

Тіло рівномірно рухається по колу зі швидкістю 31,4 м/с та обертовою частотою 2 об/с. Знайти радіус кола та період обертання тіла?​

Answer 1

Ответ:

Объяснение:

Дано:

V = 31,4 м/с

n = 2 об/с

_____________

R - ?

T - ?

Циклическая частота:

ω = 2π·n

Радиус найдем из формулы:

V = ω·R

R = V / ω = V / (2π·n)

R = 31,4 / (2·3,14·2) = 2,5 м

Период:

T = 2π·R / V

T = 2·3,14·2,5 / 31,4 = 0,5 с

Answer 2

Ответ:

v = 2pR / T ⇒ 2pR = v * T

T = 1/n = 1/2 = 0.5 с

2pR = 31.4 * 0.5 = 15.7 м

R = 15.7 / 6.28 = 2.5 м

Answer 3

Calculation of the Radius and Period of Circular Motion

To find the radius and period of the circular motion, we can use the following formulas:

Radius (r): The radius of the circle can be calculated using the formula: r = v / ω where: - v is the linear velocity of the object - ω is the angular velocity of the object

Period (T): The period of the circular motion can be calculated using the formula: T = 1 / f where: - f is the frequency of the circular motion

Now let's calculate the radius and period of the circular motion.

Given: - Linear velocity (v) = 31.4 m/s - Angular velocity (ω) = 2 rad/s

Calculating the Radius (r): Using the formula r = v / ω, we can substitute the given values: r = 31.4 m/s / 2 rad/s = 15.7 m

Therefore, the radius of the circle is 15.7 meters.

Calculating the Period (T): Since the frequency (f) is not given directly, we can use the relationship between frequency and angular velocity: f = ω / (2π)

Substituting the given angular velocity value: f = 2 rad/s / (2π) ≈ 0.3183 Hz

Using the formula T = 1 / f, we can calculate the period: T = 1 / 0.3183 Hz ≈ 3.14 seconds

Therefore, the period of the circular motion is approximately 3.14 seconds.

To summarize: - Radius (r) = 15.7 meters - Period (T) ≈ 3.14 seconds

Please note that the sources provided do not contain relevant information for this specific calculation.