Question

Здравствуйте Помогите Пожалуйста! Определите скорость автомобиля, если его колесо, радиусом 30см, за 1с делает 10 оборотов. Рассчитайте: Угловую скорость автомобиля; Частоту обращения; Период обращения; Центростремительное ускорение автомобиля; Сделайте пояснительный чертеж, на котором укажите направление нормального ускорения автомобиля.​

Answer 1

Ответ:

Объяснение:

Угловая скорость вращения, формула

Через частоту

ω=2πn

n — частота вращения (1/с)

π — число Пи (≈3,14)

ω=2*3,14*10=62,8рад/с

Частота обращению:

Частота обращения   количество оборотов в единицу времени.

Частота может быть рассчитана по формуле ν=N/t, где N-количество оборотов за время t .

ν=10/1=10c⁻¹=10Гц

Период обращения  T- время одного полного оборота.

T=t/N=1/10=0,1c

Центростремительное ускорение находим по формуле:

а=ω²*R=62,8²*0,3=1183м/с²

Answer 2

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

To determine the speed of the car, we need to calculate the linear velocity of the wheel first. The linear velocity is the distance traveled per unit of time.

Given: - Radius of the wheel (r) = 30 cm = 0.3 m - Number of revolutions made by the wheel in 1 second = 10 revolutions

To calculate the linear velocity, we can use the formula:

Linear Velocity (v) = 2πr * Number of revolutions per second

Let's calculate the linear velocity:

Linear Velocity (v) = 2π * 0.3 * 10 m/s

Using the value of π as approximately 3.14, we can calculate the linear velocity:

Linear Velocity (v) ≈ 18.84 m/s [[1]]

Now, let's calculate the other quantities:

Angular Velocity:

Angular velocity (ω) is the rate at which an object rotates around a fixed axis. It is measured in radians per second (rad/s).

Angular Velocity (ω) = 2π * Number of revolutions per second

Using the given information, we can calculate the angular velocity:

Angular Velocity (ω) = 2π * 10 rad/s

Angular Velocity (ω) = 20π rad/s

Frequency:

Frequency (f) is the number of complete revolutions or cycles per unit of time. It is measured in hertz (Hz).

Frequency (f) = Number of revolutions per second

Using the given information, we can calculate the frequency:

Frequency (f) = 10 Hz

Period:

Period (T) is the time taken to complete one full revolution or cycle. It is the reciprocal of frequency and is measured in seconds (s).

Period (T) = 1 / Frequency

Using the given information, we can calculate the period:

Period (T) = 1 / 10 s

Period (T) = 0.1 s

Centripetal Acceleration:

Centripetal acceleration (a) is the acceleration directed towards the center of the circular path. It is given by the formula:

Centripetal Acceleration (a) = (v^2) / r

Using the linear velocity and radius of the wheel, we can calculate the centripetal acceleration:

Centripetal Acceleration (a) = (18.84^2) / 0.3 m/s^2

Centripetal Acceleration (a) ≈ 1190.56 m/s^2 [[1]]

Explanation and Diagram:

The centripetal acceleration is directed towards the center of the circular path. In this case, the centripetal acceleration of the car is directed towards the center of the wheel. The direction of the centripetal acceleration is always perpendicular to the velocity vector and points towards the center of the circular path.

Here is a diagram to illustrate the direction of the centripetal acceleration:

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