Question

Диаметрт равен 10 см число оборотов 10 за 12 с найти ппериод обращения частоту вращения угловую скорость и центростримительное ускорение

Answer 1

D=10 cм => R=0.05 м
N=10
t=12 с
T-?
γ-?
ω-?
a-?

T=t/N=12/10=1.2 с
γ=N/t=10/12=0.83 c⁻¹
ω=2П/T=6.28/1.2=5.23 рад/с
a=ω²R=27.4*0.05=1.37 м/с²

Answer 2

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

To calculate the period, frequency, angular velocity, and centripetal acceleration, we need to use the given information:

- Diameter (d) = 10 cm - Number of revolutions (N) = 10 - Time (t) = 12 s

Let's calculate each value step by step:

1. Period (T): The period is the time taken for one complete revolution. It can be calculated using the formula:

T = t / N

Substituting the given values: T = 12 s / 10 = 1.2 s

2. Frequency (f): The frequency is the number of revolutions per unit time. It can be calculated using the formula:

f = 1 / T

Substituting the value of T: f = 1 / 1.2 s ≈ 0.833 Hz

3. Angular Velocity (ω): The angular velocity is the rate at which an object rotates. It can be calculated using the formula:

ω = 2π / T

Substituting the value of T: ω = 2π / 1.2 s ≈ 5.24 rad/s

4. Centripetal Acceleration (a): The centripetal acceleration is the acceleration experienced by an object moving in a circular path. It can be calculated using the formula:

a = (v^2) / r

where v is the linear velocity and r is the radius of the circular path.

To find the linear velocity (v), we need to calculate the circumference of the circle using the given diameter (d):

Circumference (C) = πd

Substituting the value of d: C = π * 10 cm ≈ 31.42 cm

The linear velocity (v) can be calculated using the formula:

v = C / t

Substituting the values of C and t: v = 31.42 cm / 12 s ≈ 2.618 cm/s

Now, substituting the values of v and r (which is half the diameter) into the formula for centripetal acceleration: a = (2.618 cm/s)^2 / (10 cm / 2) ≈ 0.6545 cm/s^2

Therefore, the calculated values are as follows:

- Period (T) ≈ 1.2 s - Frequency (f) ≈ 0.833 Hz - Angular Velocity (ω) ≈ 5.24 rad/s - Centripetal Acceleration (a) ≈ 0.6545 cm/s^2

Please note that the above calculations are based on the given information and assumptions.