An object of mass 5.0 kg is attached to a string of length 2.0 m and rotating in a horizontal circle with an angular velocity of 3.0 rad/s. What is the angular momentum of the object?
Momentum = m*V = 5 * 3 = 15 kg-rad/s.
To find the angular momentum of the object, we will use the formula:
Angular momentum = moment of inertia * angular velocity
To find the moment of inertia (I), we need to know the shape and orientation of the object. Assuming the object is a point mass rotating at a fixed distance from the center, we can use the formula for moment of inertia of a point mass:
I = m * r^2
where m is the mass of the object and r is the distance from the center of rotation. In this case, the distance is the length of the string, which is given as 2.0 m.
Now we can calculate the moment of inertia:
I = (5.0 kg) * (2.0 m)^2 = 20 kg·m^2
With the moment of inertia (I) and the given angular velocity (ω = 3.0 rad/s), we can calculate the angular momentum:
Angular momentum = (20 kg·m^2) * (3.0 rad/s) = 60 kg·m^2/s
Therefore, the angular momentum of the object is 60 kg·m^2/s.