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You spin a ball of mass 0.18 kg that is attached to a string of length 0.98 m at ω = 5.2 rad/s in a circle. What is the ball’s angular momentum?

User Dilantha
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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.

User Kgm
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