Flywheel Problem: Angular Acceleration & Linear Acceleration

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In summary, the flywheel of a steam engine has a constant angular velocity of 160 rev/min, but when steam is shut off, the friction of the bearings and of the air causes the wheel to slow down and eventually stop in 1.2 h. The constant angular acceleration of the wheel during the slowdown can be calculated using the formula \omega(t) = \omega_{0} - \epsilon t, where \omega is the angular velocity and \epsilon is the angular acceleration. The number of revolutions the wheel makes before stopping can also be calculated using this formula. Additionally, at the instant the flywheel is turning at 80.0 rev/min, the tangential component of the linear acceleration of a flywheel particle that is
  • #1
kiwinosa87
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OKie, I am having a bit of trouble with this problem...
The flywheel of a steam engine runs with a constant angular velocity of 160 rev/min. When steam is shut off, the friction of the bearings and of the air stops the wheel in 1.2 h. (a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown? (b) How many revolutions does the wheel make before stopping? (c) At the instant the flywheel is turning at 80.0 rev/min, what is the tangential component of the linear acceleration of a flywheel particle that is 38 cm from the axis of rotation? (d) What is the magnitude of the net linear acceleration of the particle in (c)?
 
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  • #2
kiwinosa87 said:
OKie, I am having a bit of trouble with this problem...
The flywheel of a steam engine runs with a constant angular velocity of 160 rev/min. When steam is shut off, the friction of the bearings and of the air stops the wheel in 1.2 h. (a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown? (b) How many revolutions does the wheel make before stopping? (c) At the instant the flywheel is turning at 80.0 rev/min, what is the tangential component of the linear acceleration of a flywheel particle that is 38 cm from the axis of rotation? (d) What is the magnitude of the net linear acceleration of the particle in (c)?

Start off with: [tex]\omega(t) = \omega_{0} - \epsilon t[/tex], where [tex]\omega[/tex] is the angular velocity, and [tex]\epsilon[/tex] the angular acceleration.
 
  • #3


First of all, it is important to understand the concept of angular acceleration and linear acceleration. Angular acceleration refers to the rate of change of angular velocity, while linear acceleration refers to the rate of change of linear velocity. In this problem, the angular acceleration of the flywheel is affected by the friction forces acting on it, which ultimately leads to a decrease in its angular velocity.

To solve this problem, we can use the formula for angular acceleration, which is given by α = (ωf - ωi)/t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time taken for the change in angular velocity.

(a) To find the constant angular acceleration, we can substitute the given values in the formula as follows:

α = (0 - 160 rev/min)/(1.2 h) = -133.33 rev/min-squared

Therefore, the constant angular acceleration of the wheel during the slowdown is -133.33 rev/min-squared.

(b) To find the number of revolutions the wheel makes before stopping, we can use the formula for angular displacement, which is given by Δθ = ωi*t + (1/2)*α*t^2, where Δθ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time taken for the change in angular velocity.

Substituting the given values, we get:

Δθ = (160 rev/min)*(1.2 h) + (1/2)*(-133.33 rev/min-squared)*(1.2 h)^2 = 144 rev

Therefore, the wheel makes 144 revolutions before stopping.

(c) To find the tangential component of the linear acceleration of a flywheel particle, we can use the formula a = r*α, where a is the tangential component of linear acceleration, r is the distance of the particle from the axis of rotation, and α is the angular acceleration.

Substituting the given values, we get:

a = (38 cm)*( -133.33 rev/min-squared) = -5066.67 cm/min-squared

Therefore, the tangential component of linear acceleration is -5066.67 cm/min-squared.

(d) To find the magnitude of the net linear acceleration of the particle, we can use the Pythagorean theorem, which states that the magnitude of
 

1. How do you calculate angular acceleration in a flywheel problem?

In order to calculate angular acceleration in a flywheel problem, you need to know the initial and final angular velocities and the time it takes for the wheel to reach the final velocity. The formula for angular acceleration is: α = (ωf - ωi) / t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time.

2. What is the relationship between angular and linear acceleration in a flywheel problem?

The relationship between angular and linear acceleration in a flywheel problem is that they are directly proportional. This means that as the angular acceleration increases, the linear acceleration will also increase. This is because the linear acceleration is dependent on the radius of the wheel, which is directly related to the angular acceleration.

3. How does the moment of inertia affect the flywheel problem?

The moment of inertia is a measure of an object's resistance to rotational motion. In a flywheel problem, the moment of inertia affects the angular acceleration. The larger the moment of inertia, the more torque is needed to accelerate the wheel to a certain angular velocity. This means that a larger moment of inertia will result in a slower angular acceleration.

4. Can the flywheel problem be solved without knowing the mass of the flywheel?

Yes, the flywheel problem can be solved without knowing the mass of the flywheel. This is because the moment of inertia is dependent on the mass, but also on the shape and distribution of the mass. As long as these values are known, the flywheel problem can be solved without knowing the mass of the flywheel.

5. How does friction affect the flywheel problem?

Friction can have a significant impact on the flywheel problem. If there is friction present, it will act against the rotation of the flywheel and decrease the angular acceleration. This means that more torque will be needed to overcome the friction and accelerate the flywheel. In some cases, friction can even cause the flywheel to stop rotating altogether.

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