Unwinding a string around a spool, what is the angular acceleration?

[mustang]

Problem 5. given:g=9.81m/s^2.
A light string 1.20 m long is wrapped around a solid cylindrical spool with a redius of 0.0195 m and a mass of 0.380 kg. A 8.40 kg mass is then attached to the free end of the string, causing the string to unwind from the spool.
a. What is the angular acceleration of the spool? Answer in rad/s^2.
Note : I worked on the problem and I got 22241.14162 by using the formula (moment of inertia* angular acceleration= mass*g*radius. However my answer was wrong what did I do wrong?

 

[Doc Al]

Originally posted by mustang

Note : I worked on the problem and I got 22241.14162 by using the formula (moment of inertia* angular acceleration= mass*g*radius. However my answer was wrong what did I do wrong?

You are assuming that the tension in the string (which is what is pulling on the spool) equals the weight of the mass.

To do this problem correctly, treat each object separately. Consider the forces acting on each body, and write down the equations describing each. You'll have two equations and two unknowns. And the right answer.

 

[M98Ranger]

Based on the given information, the angular acceleration of the spool can be calculated using the formula: moment of inertia * angular acceleration = mass * g * radius. In this case, the moment of inertia can be calculated as I = 1/2 * m * r^2, where m is the mass of the spool and r is the radius. Substituting the given values, we get I = 1/2 * 0.380 kg * (0.0195 m)^2 = 3.5715e-5 kg*m^2.

Next, we can rearrange the formula to solve for angular acceleration: angular acceleration = (mass * g * radius) / moment of inertia. Substituting the given values, we get angular acceleration = (8.40 kg * 9.81 m/s^2 * 0.0195 m) / 3.5715e-5 kg*m^2 = 459.917 rad/s^2.

Therefore, the angular acceleration of the spool is approximately 459.917 rad/s^2. It is possible that your answer of 22241.14162 was incorrect because you may have used the incorrect value for the moment of inertia or made a calculation error. Double-checking your calculations can help identify any mistakes.