Question

Материальная точка движется по окружности радиуса 50 см со скоростью 2 м/с . Найдите период колебаний, частоту ,угловую скорости и нррмальное ускорение.

Answer 1

1)
Период:
T = 2π*R / V = 6,28*0,50/2 = 1,57 с
2)
Частота:
v = 1 / T = 1 / 1,57 = 0,64 Гц
3)
Угловая скорость:
ω = 2π/T = 6,28/1,57 = 4 рад/с
4)
Нормальное ускорение:
a = V² / R = 2²/0,5 = 8 м/с²

Answer 2

Calculation of Period, Frequency, Angular Velocity, and Centripetal Acceleration

To find the period, frequency, angular velocity, and centripetal acceleration of a material point moving in a circle with a radius of 50 cm and a speed of 2 m/s, we can use the following formulas:

1. Period (T): The time taken for one complete revolution. 2. Frequency (f): The number of complete revolutions per unit time. 3. Angular Velocity (ω): The rate at which the angle changes with time. 4. Centripetal Acceleration (a): The acceleration towards the center of the circle.

Let's calculate each of these values step by step.

Period (T)

The period is the time taken for one complete revolution. It can be calculated using the formula:

T = 2πr/v

where: - T is the period, - π is a mathematical constant approximately equal to 3.14159, - r is the radius of the circle, and - v is the speed of the material point.

Substituting the given values: - r = 50 cm = 0.5 m - v = 2 m/s

T = 2π(0.5 m) / (2 m/s)

Simplifying the equation: T = π s

Therefore, the period of the material point is π seconds.

Frequency (f)

The frequency is the number of complete revolutions per unit time. It can be calculated using the formula:

f = 1/T

where: - f is the frequency, and - T is the period.

Substituting the value of T from the previous calculation: f = 1 / (π seconds)

Therefore, the frequency of the material point is 1/π Hz.

Angular Velocity (ω)

The angular velocity is the rate at which the angle changes with time. It can be calculated using the formula:

ω = v/r

where: - ω is the angular velocity, - v is the speed of the material point, and - r is the radius of the circle.

Substituting the given values: - v = 2 m/s - r = 50 cm = 0.5 m

ω = (2 m/s) / (0.5 m)

Simplifying the equation: ω = 4 rad/s

Therefore, the angular velocity of the material point is 4 rad/s.

Centripetal Acceleration (a)

The centripetal acceleration is the acceleration towards the center of the circle. It can be calculated using the formula:

a = v^2 / r

where: - a is the centripetal acceleration, - v is the speed of the material point, and - r is the radius of the circle.

Substituting the given values: - v = 2 m/s - r = 50 cm = 0.5 m

a = (2 m/s)^2 / (0.5 m)

Simplifying the equation: a = 8 m/s^2

Therefore, the centripetal acceleration of the material point is 8 m/s^2.

To summarize: - The period of the material point is π seconds. - The frequency of the material point is 1/π Hz. - The angular velocity of the material point is 4 rad/s. - The centripetal acceleration of the material point is 8 m/s^2.

Please let me know if there's anything else I can help you with!