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Mars2501 [29]
3 years ago
5

A energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.0 MJ when the flywheel is rotating at 20,

000 revolutions per minute. What is the moment of inertia of the flywheel?
Physics
1 answer:
mariarad [96]3 years ago
8 0

Answer:

Moment of inertia of the flywheel, I=1.82\ kg-m^2          

Explanation:

Given that,

The maximum energy stored on  flywheel, E=4\ MJ=4\times 10^6\ J

Angular velocity of the flywheel, \omega=20000\ rev/s=2094.39\ rad/s

We need to find the moment of inertia of the flywheel. The energy of a flywheel in rotational kinematics is given by :

E=\dfrac{1}{2}I\omega^2

I is the moment of inertia of the flywheel

On rearranging we get :

I=\dfrac{2E}{\omega^2}

I=\dfrac{2\times 4\times 10^6}{(2094.39)^2}

I=1.82\ kg-m^2

So, the moment of inertia of the flywheel is I=1.82\ kg-m^2. Hence, this is the required solution.

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Structures on a bird feather act like a diffraction grating having 8000 8000 lines per centimeter. What is the angle of the firs
sammy [17]

Answer:

Angle of first order maximum, \theta=21.19^{\circ}

Explanation:

Given that,

Wavelength of the light, \lambda=452\ nm=452\times 10^{-9}\ m

Number of lines, N = 8000 per cm

The relation between the number of lines and the slit width is given by :

d=\dfrac{1}{N}

d=\dfrac{1}{8000/cm}  

d=0.000125\ cm=1.25\times 10^{-6}\ m

The equation of grating is given by :

d\ sin\theta=n\lambda

n = 1

sin\theta=\dfrac{\lambda}{d}

sin\theta=\dfrac{452\times 10^{-9}}{1.25\times 10^{-6}}

\theta=21.19^{\circ}

So, the angle of the first-order maximum is 21.19 degrees. Hence, this is the required solution.

6 0
3 years ago
You have a horizontal grindstone (a disk) that is 86 kg, has a 0.33 m radius, is turning at 92 rpm (in the positive direction),
Rudiy27

Answer:

a) α = 0.338 rad / s²  b)   θ = 21.9 rev

Explanation:

a) To solve this exercise we will use Newton's second law for rotational movement, that is, torque

    τ = I α

    fr r = I α

Now we write the translational Newton equation in the radial direction

    N- F = 0

    N = F

The friction force equation is

    fr = μ N

    fr = μ F

The moment of inertia of a saying is

    I = ½ m r²

Let's replace in the torque equation

    (μ F) r = (½ m r²) α

    α = 2 μ F / (m r)

    α = 2 0.2 24 / (86 0.33)

    α = 0.338 rad / s²

b) let's use the relationship of rotational kinematics

    w² = w₀² - 2 α θ

    0 = w₀² - 2 α θ

    θ = w₀² / 2 α

Let's reduce the angular velocity

     w₀ = 92 rpm (2π rad / 1 rev) (1 min / 60s) = 9.634 rad / s

    θ = 9.634 2 / (2 0.338)

     θ = 137.3 rad

Let's reduce radians to revolutions

    θ = 137.3 rad (1 rev / 2π rad)

    θ = 21.9 rev

7 0
3 years ago
How long has eggs been around
Paraphin [41]

Answer:

About six million years

Explanation:

3 0
3 years ago
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Watching television, with theremote control in your hand, which of the following exerts the greatest gravitational force on you?
natulia [17]
A. The couch you are sitting on
3 0
3 years ago
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One violin creates a sound whose intensity level is 60dB. Find the intensity level of 16 violins, each playing at this intensity
Yanka [14]

Answer:

72.04 dB.

Explanation:

The intensity level of 60dB corresponds to the sound intensity I given by the equation

60dB = 10log(\dfrac{I}{I_0} )

where I_0 = 1*10^{-12}W/m^2

solving for I we get:

6 = log(\dfrac{I}{I_0} )

10^6 =\dfrac{I}{1*10^{-12}}

\boxed{I = 1*10^{-6} W/m^2}

Now, when 16 violins are playing the intensity I becomes

{I = 16(1*10^{-6} W/m^2)

which on the decibel scale gives

dB = 10log(\dfrac{16*10^{-6}}{1*10^{-12}} )

dB = 72.04\: dB.

Thus, playing 16 violins together gives the intensity level of 72 dB.

8 0
3 years ago
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