Final answer:
The ball's angular momentum is approximately 0.89856 kg·m^2/s when spun at an angular velocity of 5.2 rad/s with a string length of 0.98 m and mass of 0.18 kg.
Step-by-step explanation:
To calculate the ball’s angular momentum, we'll use the formula:
L = I × ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
The moment of inertia (I) of a point mass (m) at a distance (r) from the axis of rotation is:
I = m × r2
Given a mass (m) of 0.18 kg and a string length (r) of 0.98 m, and an angular velocity (ω) of 5.2 rad/s, we get:
I = 0.18 kg × (0.98 m)2 = 0.18 kg × 0.9604 m2 ≈ 0.1728 kg · m2
Therefore, the angular momentum (L) is:
L = 0.1728 kg · m2 × 5.2 rad/s ≈ 0.89856 kg · m2/s
The ball's angular momentum when attached to a string and spun at an angular velocity of 5.2 rad/s is approximately 0.89856 kg · m2/s.