# Calculating Angular Velocity of 0.600 m Flywheel

• masterthephysics
In summary: Then use the equation K = .5 I omega^2.In summary, the problem involves a flywheel with a diameter of 0.600 m, a rope wrapped around it, and a steady pull of 40.0 N being exerted on the rope. The flywheel starts from rest and 5.00 m of rope are unwound in 2.00 s. The question involves finding the angular acceleration of the flywheel and using it to calculate the final kinetic energy. The process involves finding the average velocity and using it to find the final angular velocity, then using the relationship \theta = \frac{\alpha t^2}{2} to find the angular acceleration. From there, the moment of inertia is
masterthephysics
Question:
A flywheel 0.600 m in diameter pivots on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 40.0 N is exerted on the rope. The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.

Okay i have tried finding the angular velocity by first finding the linear velocity=5/2 then putting it into v=omega*r and making omega the subject. Then after finding omega I substituted it into the equation of (omega - 0)/2 but its wrong :(

Where have I gone wrong? Can someone help me out? thanks in advance

masterthephysics said:
Question:
A flywheel 0.600 m in diameter pivots on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 40.0 N is exerted on the rope. The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.

Okay i have tried finding the angular velocity by first finding the linear velocity=5/2 then putting it into v=omega*r and making omega the subject. Then after finding omega I substituted it into the equation of (omega - 0)/2 but its wrong :(

Where have I gone wrong? Can someone help me out? thanks in advance

You have not actually stated the question you are trying to answer. Something about acceleration I bet. In any case, you have probably confused average velocity with final velocity. The information given in the problem gives you the average velocity. From that you have to decuce final velocity and probably use that to find acceleration.

What is the angular acceleration of the flywheel?

i got 4.17 as angular accerleration but it was wrong

Acceleration = Velocity / Time.. you found the velocity, you have the time..

would that give me the tangential acceleration?
the i can work out a_tan = r*alpha?
alpha = angular acceleration

Alternatively if oyu can find the angle swept during the 2s, you can find the acceleration using the relationship

$$\theta = \frac{\alpha t^2}{2}$$

masterthephysics said:
i got 4.17 as angular accerleration but it was wrong

Either you have confused the average and final velocity, or used the given diameter instead of the radius in your calculation.

so to work out theta i would use s=r*theta with s=5 and r=0.3?

masterthephysics said:
so to work out theta i would use s=r*theta with s=5 and r=0.3?

That would be correct for using

$$\theta = \frac{\alpha t^2}{2}$$

You can also do it using your original velocity calculation, but you need to understand that is the average velocity, which is 1/2 the final velocity.

alright - i tried using the equation above with theta but I still get the wrong answer for the acceleration: i did -
5/0.3 = (alpha(4))/2 and got 8.33

masterthephysics said:
alright - i tried using the equation above with theta but I still get the wrong answer for the acceleration: i did -
5/0.3 = (alpha(4))/2 and got 8.33

That looks right.. what are they giving as the correct answer?

By velocity it would be average velocity = 5m/2 sec = 2.5m/sec. So omega = v/r = 5m/2sec/.3m = 8.33/sec. The final angular velocity would be twice that and the time to reach that angular velocity is 2 seconds

alpha = 2*8.33/sec/2sec = 8.33/sec^2

Last edited:
thanks! i just realized that i did something wrong haha

how would u work out the final kinetic energy here?
i tried using k_e=.5*I*(omega)^2

but I is an unknown, as to find I, u use I=kmr2, so I=(1/2)*m*(.03)^2 (as this is a solid cylinder)
and i hav no idea how to work out m.

wait can u use f=ma? so 40 n = m* a, where a =r*alpha, or=2.499

so 40=m*2.499 and m=16.01kg?

Last edited:
You would need the mass to find kinetic energy.

la673 said:
how would u work out the final kinetic energy here?
i tried using k_e=.5*I*(omega)^2

but I is an unknown, as to find I, u use I=kmr2, so I=(1/2)*m*(.03)^2 (as this is a solid cylinder)
and i hav no idea how to work out m.

wait can u use f=ma? so 40 n = m* a, where a =r*alpha, or=2.499

so 40=m*2.499 and m=16.01kg?

If you have found the angular deceleration correctly, you now have everything needed to figure out I, and you need to do it.

## 1. How do I calculate the angular velocity of a 0.600 m flywheel?

To calculate the angular velocity of a flywheel, you can use the formula: ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the radius of the flywheel. In this case, the radius is given as 0.600 m, so you would need to determine the linear velocity of the flywheel to calculate the angular velocity.

## 2. What is the linear velocity of a 0.600 m flywheel?

The linear velocity of a flywheel can be calculated using the formula: v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity. In this case, the radius is given as 0.600 m, so you would need to determine the angular velocity to calculate the linear velocity.

## 3. How do I determine the radius of a 0.600 m flywheel?

The radius of a flywheel is the distance from the center of the flywheel to its outer edge. In this case, it is given as 0.600 m. If the radius is not given, you can measure it using a ruler or other measuring tool.

## 4. What units are used to measure angular velocity?

Angular velocity is typically measured in radians per second (rad/s) or revolutions per minute (rpm). Make sure to use the appropriate units in your calculation.

## 5. How does the angular velocity of a flywheel affect its performance?

The angular velocity of a flywheel determines how fast it can rotate and how much energy it can store. A higher angular velocity means the flywheel can store more energy and release it more quickly. However, too high of an angular velocity can also cause the flywheel to become unbalanced and potentially lead to mechanical issues.

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