Question

Диск радиусом 60 см вращается относительно оси, проходящей через центр диска с частотой 30 об./мин. Чему равна равна линейная скорость точек диска, наиболее отдалённых от его центра?

Answer 1

Ответ:

Объяснение:

Дано:

R = 60 см = 0,60 м

n = 30 об/мин = 0,5 об/с

_____________

V - ?

Циклическая частота:

ω = 2π·n

Линейная скорость:

V = ω·R

V = 2π·n·R = 2·3,14·0,5·0,60 ≈ 1,9 м/с

Answer 2

Calculation of Linear Velocity

To calculate the linear velocity of points on a disk, we need to know the radius of the disk and the angular velocity of its rotation.

Given: - Radius of the disk = 60 cm - Angular velocity = 30 revolutions per minute (rpm)

To find the linear velocity of the points on the disk that are farthest from its center, we can use the formula:

Linear velocity = Radius × Angular velocity

Let's calculate the linear velocity using the given values:

Radius = 60 cm

Angular velocity = 30 rpm

Linear velocity = 60 cm × 30 rpm

Converting the angular velocity from revolutions per minute to radians per second:

Angular velocity = 30 rpm × (2π radians / 1 revolution) × (1 minute / 60 seconds)

Simplifying the units:

Angular velocity = 30 × 2π / 60 radians per second

Angular velocity = π radians per second

Now, substituting the values into the formula:

Linear velocity = 60 cm × π radians per second

Calculating the linear velocity:

Linear velocity ≈ 188.5 cm/s

Therefore, the linear velocity of the points on the disk that are farthest from its center is approximately 188.5 cm/s.