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.

SPHY001 Practice Quiz - Unit 10 | LA050

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?

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