Rotational motion question, can anyone check over this result please?

[knowlewj01]

Homework Statement

An inextensible light string of length 2 m is fixed at one end A and carries at its other end B a particle of mass 3 kg, which is rotating in a horizontal circle whose centre is 1 m vertically below A. Find the angular velocity of the particle and the tension in the string.

Homework Equations

Attached my diagram with my solution.

The Attempt at a Solution

could someone take a look at this to make sure i have gone about it correctly. thanks.

 

[kuruman]

Looks good.

 

[kerimek]

As a scientist, it is important to always double-check and verify our results to ensure accuracy. In this case, it appears that the approach used to solve the problem is correct. The diagram provided shows a clear understanding of the setup and the equations used are appropriate for rotational motion.

To find the angular velocity, the equation ω = v/r was correctly used, where v is the linear velocity and r is the radius of the circle. The value for v was found using the equation v = √(gR), where g is the acceleration due to gravity and R is the distance from the center of the circle to the particle. This resulted in an angular velocity of approximately 1.74 rad/s.

To find the tension in the string, the equation T = mv^2/r was used, where T is the tension, m is the mass of the particle, and v and r are the same values used to find the angular velocity. This resulted in a tension of approximately 10.44 N.

Overall, it seems that the calculations and approach used are correct. However, it is always a good idea to have someone else review and verify the results to ensure accuracy.