Physics help angular velocity and inertia

[Dawg]

Homework Statement

2 questions I really need help with
1) a 20g weight is attached to one free end of a 2.5m length of string, other end is attached to the ceiling. The weight is pulled to one side And released when the angle between the verticle and the string is 53.1 degrees. What is the angular velocity ofthe weight when the angular acceleration is zero

2) a uniform disc of radius 0.25m is attached to a thread of mass of 5kg. The disc has mass 10kg calculate the moment of inertia of the disc. Thanks very much any help greatly appreciated

Homework Equations

The Attempt at a Solution

 

[zack_21]

These both can easily be solved with the appropriate equations.

 

[tomcue]

1) The angular velocity of the weight can be calculated using the formula:

ω = √(g/L * sinθ)

Where g is the acceleration due to gravity (9.8 m/s^2), L is the length of the string (2.5m), and θ is the angle between the vertical and the string (53.1 degrees). Substituting these values, we get an angular velocity of approximately 3.05 rad/s.

2) The moment of inertia of the disc can be calculated using the formula:

I = 1/2 * m * r^2

Where m is the mass of the disc (10kg) and r is the radius of the disc (0.25m). Substituting these values, we get a moment of inertia of 0.625 kg*m^2.