# Circular Constant Acceleration Formula

• CyclicCircle
In summary, the conversation discusses finding the speed of a stationary, uniform circular flywheel after completing 25 revolutions when a constant tangential force of magnitude 12N is applied. The correct approach involves calculating the torque and moment of inertia, and using the formula for angular acceleration to find the final velocity. The error in the previous approach was using the formula for a ring instead of a disc, leading to an incorrect answer.
CyclicCircle
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A constant tangential force of magnitude 12N is applied to the rim of a stationary, uniform circular flywheel of mass 100kg and radius 0.5m. Find the speed at which the flywheel is rotating after it has completed 25 revolutions?

I know that this can be done using work-energy. But since a constant tangential force is applied, I tried using kinematic equations.

Initial angular velocity $\omega = 0$, angular displacement $\theta = 25 \times 2\pi = 50\pi$.

If $\alpha$ is the angular acceleration, $mr\alpha = 12$, $(100)(0.5)\alpha = 12$, $\alpha = 0.24$.

Final velocity $\Omega^2 = \omega^2 + 2\alpha \theta$, which gives $\Omega = 8.68$. But the correct answer is apparently 12.3.

It is not clear what you are doing in the second last line.

First calculate the Torque ##\tau## applied by the force to the flywheel.
Then find the Moment of Inertia ##I## of the flywheel.
Then the angular acceleration is ##\alpha=\tau/I##. It is not 0.24.

If you do this and then substitute into the last line of your post, you should get 12.3.

CyclicCircle
Thank you so much.

I used the fact that tangential acceleration = radius*(angular acceleration) and F = ma to obtain force = mass*radius*(tangential acceleration). What is the error in this?

CyclicCircle said:
Thank you so much.

I used the fact that tangential acceleration = radius*(angular acceleration) and F = ma to obtain force = mass*radius*(tangential acceleration). What is the error in this?
It is a disc, not a ring. You need to use the right formula for its moment of inertia.

CyclicCircle
Thanks. I completely forgot about mass distribution!

## 1. What is the formula for calculating circular constant acceleration?

The formula for calculating circular constant acceleration is a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius.

## 2. How is circular constant acceleration different from linear acceleration?

Circular constant acceleration refers to the acceleration of an object moving in a circular path, while linear acceleration refers to the acceleration of an object moving in a straight line. Circular acceleration involves a change in direction, while linear acceleration involves a change in speed.

## 3. What are the units of measurement for circular constant acceleration?

The units of measurement for circular constant acceleration are meters per second squared (m/s^2).

## 4. How is circular constant acceleration related to centripetal force?

Circular constant acceleration is related to centripetal force through the formula F = ma, where F is the centripetal force, m is the mass of the object, and a is the circular constant acceleration. This means that the force required to keep an object moving in a circular path is directly proportional to the mass and acceleration of the object.

## 5. Can circular constant acceleration be negative?

Yes, circular constant acceleration can be negative. This indicates that the object is slowing down or changing direction in a counterclockwise direction. A positive acceleration indicates that the object is speeding up or changing direction in a clockwise direction.

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