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Introductory Physics Homework Help
Uniform Circular Motion, Acceleration problem
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[QUOTE="No1_129848, post: 5758693, member: 622959"] [h2]Homework Statement [/h2] A cat rides a merry-go-round turning with uniform circular motion. At time t[SUB]1[/SUB] = 2.00 s, the cat’s velocity is V[SUB]1[/SUB] = (3.00 m/s)i + (4.00 m/s)j , measured on a horizontal xy coordinate system. At t[SUB]2[/SUB] = 5.00 s, the cat’s velocity is V[SUB]2[/SUB] = (3.00 m/s)i + (4.00 m/s)j. What are (a) the magnitude of the cat’s centripetal acceleration and (b) the cat’s average acceleration during the time interval t[SUB]2[/SUB] - t[SUB]1[/SUB], which is less than one period? [h2]Homework Equations[/h2] [/B] T = 2πr/V a = V[SUP]2[/SUP]/r [h2]The Attempt at a Solution[/h2] [/B] So, the first thing I did was sketch the situation, and the vectors seem to be on the opposite end of the circumference, so i tested for that: V[SUB]1[/SUB] * V[SUB]2[/SUB] = V[SUB]1x[/SUB] * V[SUB]2x[/SUB] + V[SUB]1y[/SUB] * V[SUB]2y[/SUB] = 3*(-3) + 4*(-4) = -25 V[SUB]1[/SUB] * V[SUB]2[/SUB] = V[SUB]1[/SUB] * V[SUB]2[/SUB] CosΘ = √3[SUP]2[/SUP]+4[SUP]2[/SUP]*√(-3)[SUP]2[/SUP]+(-4)[SUP]2[/SUP] = 25 CosΘ → CosΘ = -1 → Θ = Cos[SUP]-1[/SUP](-1) = 180° So it's proven that the cat is in two different positions that cover half of the circumference, which means that Δt = ½T Δt = t[SUB]2[/SUB]-t[SUB]1[/SUB] = 5s-2s = 3s T = 2Δt = 3s * 2 = 6s T = 2πr/V → r = TV/2π = 6s * 5 m/s / 2π = 4,8 m a = V[SUP]2[/SUP]/r → (5 m/s)[SUP]2[/SUP]/4,8 m = 5,2 m/s[SUP]2[/SUP] So this should answer the first part of the problem, now I'm asked to find the average acceleration, and I'm not sure what approach is the correct one, I know the equation for the average acceleration is: a[SUB]avg[/SUB] = V[SUB]2[/SUB] - V[SUB]1[/SUB] / t[SUB]2[/SUB] - t[SUB]1[/SUB] And I am not sure if I should consider just the magnitude of the two velocities, which means that a[SUB]avg[/SUB] = 0, or if I should solve in unit vector notation, doing the following: a[SUB]avg[/SUB] = V[SUB]2[/SUB] - V[SUB]1[/SUB] / t[SUB]2[/SUB] - t[SUB]1[/SUB] = (-3-3)i + (-4-4)j / 3s = -2i -2,67j → a[SUB]avg[/SUB] = √(-2)[SUP]2[/SUP]+(-2,67)[SUP]2[/SUP] = 3,3 m/s[SUP]2[/SUP] What is the correct way to answer the second question? (also, kinda off topic, is there a way to write fractions and vectors on the forum?) Thanks in advance, Ivan. [/QUOTE]
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Introductory Physics Homework Help
Uniform Circular Motion, Acceleration problem
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