A child swings a 0.38 kg ball in a circle on a string that is 1.3 m long. If the ball makes 1.2 rev/s, what is the magnitude of the ball's angular momentum?

Question

BlackTom AI · Accepted Answer

We start by identifying the relevant formulae for circular motion and angular momentum. For a point mass m moving in a circle of radius r, the angular momentum is L = I ω, and since the mass is concentrated at the ball, I = m r^2, so L = m r^2 ω. The angular speed ω must be in radians per second, not revolutions per second.

Option 1: 5.3 kg·m^2/s. To assess this, compute the expected L using the given values. Convert the frequency: 1.2 rev/s × 2π rad/rev = 2.4π rad/s ≈ 7.54 rad/s. Then m r^2 ω = 0.38 × (1.3)^2 × 7.54. (1.3)^2 = 1.69, and 0.38 × 1.69 ≈ 0.642. Multiplying 0.642 by 7.54 gives ≈ 4.84. This is smaller than 5.3, so option 1 is not a precise match to the calculation.

Option 2: 4.8 kg·m^2/s. From the same computation above, 0.642 × 7.54 ≈ 4.84, which is very close to 4.8 when rounded to two significant figures. Given typical measurement or rounding in problems, 4.8 is a plausible match to the calculated value.

Option 3: 0.8 kg·m^2/s. This is far from the computed 4.84. To reach 0.8, the product m r^2 would have to be much smaller, or the angular speed almost an order of magnitude smaller, which does not align with the provided numbers.

Option 4: 3.8 kg·m^2/s. This value is less than the computed 4.84 by about 1 unit, suggesting either a significantly smaller r, m, or ω. Since r and m are fixed by the problem and ω is fixed by the given frequency, this option is inconsistent with the calculation.

Summary: The correct approach yields L = m r^2 ω = 0.38 × (1.3)^2 × (1.2 × 2π) ≈ 4.84 kg·m^2/s. Among the offered choices, 4.8 kg·m^2/s is the closest match to the calculated value, making it the best option. The other options deviate noticeably from the correct magnitude or rely on incorrect unit handling or numeric estimates.

A child swings a 0.38 kg ball in a circle on a string that is 1.3 m long. If the ball makes 1.2 rev/s, what is the magnitude of the ball's angular momentum? 单项选择题

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