A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance r₁ from the center of the disk and point 2 on the disk is located at a distance r₂ from the center of the disk.If r₂ = 2r₁,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time. A)ω₂/ω₁ B)α₂/α₁ C)a_c₂/ac₁ D)All the ratios are 1 so none is larger.

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Quizplus · Accepted Answer

Since the angular velocity (ω) is the same for all points on the disk and the angular acceleration (α) is also the same for all points (because ω is increasing at a constant rate), the ratios in options A and B are both 1. However, the centripetal acceleration (a_c) depends on the radius (r) and the square of the angular velocity (ω^2), as given by the formula a_c = rω^2. Since point 2 is twice as far from the center as point 1 (r2 = 2r1), the centripetal acceleration at point 2 (a_c2) will be larger than that at point 1 (a_c1) by a factor of 2^2 = 4, making the ratio in option C the largest.

A Circular Disk Is Rotating About a Central Axis with an Angular