This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
a) Step 1: Calculate the angular momentum L. The angular momentum L is the cross product of the position vector r and the momentum vector p. Given r = (4, 5, 3) and p = (1, 4, 2). L = r × p = i & j & k \\ 4 & 5 & 3 \\ 1 & 4 & 2 L = (5 · 2 - 3 · 4)i - (4 · 2 - 3 · 1)j + (4 · 4 - 5 · 1)k L = (10 - 12)i - (8 - 3)j + (16 - 5)k L = -2i - 5j + 11k The angular momentum is (-2, -5, 11). Step 2: Calculate the dot product of r and p. The dot product is used to find the angle between the vectors. r · p = (4)(1) + (5)(4) + (3)(2) r · p = 4 + 20 + 6 = 30 Step 3: Calculate the magnitudes of r and p. |r| = sqrt(4^2 + 5^2 + 3^2) = sqrt(16 + 25 + 9) = sqrt(50) |p| = sqrt(1^2 + 4^2 + 2^2) = sqrt(1 + 16 + 4) = sqrt(21) Step 4: Calculate the angle between r and p. The angle is given by = r · p|r| |p|. = (30)/(sqrt(50) 21) = (30)/(sqrt(1050)) = ((30)/(sqrt(1050))) ≈ (0.92582) ≈ 22.20^ Send me the next one 📸