What is the angular momentum of a 0.705kg ball rotating on the end of a thin string in a circle of radius 0.800m at an angular speed of 12.8rad/s ?
To calculate the angular momentum of a rotating object, we use the formula:
Angular momentum (L) = moment of inertia (I) × angular speed (ω)
First, we need to find the moment of inertia of the ball. The moment of inertia depends on the shape and mass distribution of the object. In this case, the ball is rotating on the end of a thin string, so we can assume it is a point mass.
For a point mass rotating in a circular path, the moment of inertia is given by:
I = m × r^2
where m is the mass of the object and r is the radius of the circular path.
In this case, the mass of the ball is 0.705 kg, and the radius of the circular path is 0.800 m. So we can substitute these values into the equation:
I = 0.705 kg × (0.800 m)^2
Calculating this gives us the moment of inertia:
I = 0.450 kg·m^2
Next, we need to find the angular momentum by multiplying the moment of inertia by the angular speed:
L = I × ω
Substituting the values we calculated:
L = 0.450 kg·m^2 × 12.8 rad/s
Calculating this gives us the angular momentum:
L = 5.76 kg·m^2/s
So, the angular momentum of the ball is 5.76 kg·m^2/s.