Calculate the angular momentum of a 1.75 kg ball rotating on the end of a thin string in a circle of radius 3.5 and an angular speed of 11 rad /s. Treat the ball as a point.
To calculate the angular momentum of the ball, we can use the formula:
Angular momentum = moment of inertia × angular velocity
First, let's calculate the moment of inertia of the ball. Since we are treating the ball as a point, we can use the formula for the moment of inertia of a point mass rotating about an axis:
Moment of inertia (I) = mass (m) × radius squared (r²)
Given:
Mass of the ball (m) = 1.75 kg
Radius (r) = 3.5 m
Plugging in these values, we get:
I = (1.75 kg) × (3.5 m)²
I = 21.4375 kg·m²
Now, let's calculate the angular momentum using the given angular velocity:
Angular velocity (ω) = 11 rad/s
Angular momentum (L) = I × ω
L = (21.4375 kg·m²) × (11 rad/s)
L = 235.8125 kg·m²/s
Therefore, the angular momentum of the ball is 235.8125 kg·m²/s.