Angular Acceleration of a rotating wheel

• TrippingBilly
In summary, the rotating wheel is not starting from rest, which was not taken into consideration in the initial attempts to calculate the constant angular acceleration. After further consideration, the correct calculation for the acceleration is 20.99, which was discovered by converting 37 revolutions to 74 pi and solving for acceleration.
TrippingBilly
A rotating wheel requires 2.98 s to rotate through 37.0 revolutions. Its angular speed at the end of the 2.98 s interval is 98.8 rad/s. What is the constant angular acceleration of the wheel?

First I tried acceleration = (98.8rad/s - 0 rad/s) / 2.98 s - 0s = 33.15, which was incorrect.

Then I tried acceleration = (98.8rad/sec)^2 - (0 rad/sec)^2 = 2 * acceleration * 74pi and solving for acceleration i got 20.99 but that's incorrect too. I got 74 pi by converting 37 rev.

Any clue as to what I'm doing wrong?

TrippingBilly said:
A rotating wheel requires 2.98 s to rotate through 37.0 revolutions. Its angular speed at the end of the 2.98 s interval is 98.8 rad/s. What is the constant angular acceleration of the wheel?

First I tried acceleration = (98.8rad/s - 0 rad/s) / 2.98 s - 0s = 33.15, which was incorrect.

Then I tried acceleration = (98.8rad/sec)^2 - (0 rad/sec)^2 = 2 * acceleration * 74pi and solving for acceleration i got 20.99 but that's incorrect too. I got 74 pi by converting 37 rev.

Any clue as to what I'm doing wrong?
If all the information given in the problem is correct, the wheel is not starting from rest.

Huh, I guess I never considered that. That's frustrating :\ Thanks for your help though :)

never mind, i got it :)

Last edited:
TrippingBilly said:
never mind, i got it :)

I thought you had it when you posted your previous reply. Sorry if you were expecting something more.

TrippingBilly said:
Huh, I guess I never considered that. That's frustrating :\ Thanks for your help though :)

Oh no, I stopped looking at the problem for a while. But I decided to come back to it, and I had posted another question, but in the meantime I figured out the answer so I edited my post to the one you quoted. No worries :)

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity, which is the speed at which a rotating object is spinning around a fixed axis. It is measured in radians per second squared (rad/s²).

2. How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is α = (ω₂ - ω₁) / (t₂ - t₁), where α is the angular acceleration, ω is the angular velocity, and t is the time.

3. What factors affect the angular acceleration of a rotating wheel?

The angular acceleration of a rotating wheel is affected by the net torque applied to the wheel, the moment of inertia of the wheel, and the distribution of mass within the wheel. The net torque can be increased by applying a larger force or increasing the distance from the axis of rotation. A larger moment of inertia or a more spread out mass distribution will result in a smaller angular acceleration.

4. Can angular acceleration be negative?

Yes, angular acceleration can be negative. A negative angular acceleration means that the angular velocity is decreasing over time, which can occur when the net torque is in the opposite direction of the spin of the wheel. This can happen when a braking force is applied to a rotating wheel.

5. How does angular acceleration relate to linear acceleration?

Angular acceleration and linear acceleration are related through the radius of rotation. The linear acceleration of a point on the outer edge of a rotating wheel is equal to the angular acceleration multiplied by the radius of the wheel. This relationship is described by the formula a = αr, where a is the linear acceleration, α is the angular acceleration, and r is the radius of rotation.

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