# Calculating Alpha: Magnitude of Angular Acceleration??

• merlos
Therefore, the acceleration of the block is not equal to g, but is actually equal to the magnitude of the tangential acceleration of the cylinder (since the block is moving with the cylinder). This tangential acceleration can be found using the formula a = r x alpha, where r is the radius of the cylinder and alpha is the angular acceleration of the cylinder. Therefore, in summary, the magnitude alpha of the angular acceleration of the cylinder can be found using the formula alpha = 2g/r.
merlos
calculating alpha??

A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure. The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.

Find the magnitude alpha of the angular acceleration of the cylinder as the block descends.
Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

Acceleration of the block is = g
Force acting on the block is = mg
The torque by this force on the cylinder about the axis = mgr
This results in accelerating the rotation of the cylinder.
mgr = I x alpha, where I = moment of inertia of the solid cylinder;
alpha = Angular acceleration of the cylinder.

I = (1/2)mr^2

alpha = torque/I = mgr/I = 2g/r
??

merlos said:
Acceleration of the block is = g
Force acting on the block is = mg
That would be true if the block was in free fall. But I assume it's tied to the string that's wrapped around the cylinder.

## 1. What is alpha in physics?

Alpha, or α, is a symbol used to represent the magnitude of angular acceleration in physics. It is a measure of how quickly an object's angular velocity changes over time.

## 2. How is alpha calculated?

Alpha is calculated by dividing the change in angular velocity by the change in time. It can also be calculated by taking the second derivative of the object's angular displacement with respect to time.

## 3. What are the units of alpha?

The units of alpha are radians per second squared (rad/s²) in the SI system. In the imperial system, it is measured in degrees per second squared (°/s²).

## 4. How is alpha related to angular velocity?

Alpha and angular velocity are closely related, as alpha is the rate of change of angular velocity over time. This means that the greater the value of alpha, the faster the object's angular velocity is changing.

## 5. What is the significance of calculating alpha?

Calculating alpha is important in understanding the motion of rotating objects and how quickly they are accelerating. It is also essential in analyzing the forces and torques acting on a rotating object.

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