Question

lucia wants to change the motion map shown so that it shows uniform circular motion. what change should lucia make? she should change the length of each vector that is tangent to the circle so that it is the same as the vector pointing toward the center at that point. she should change the direction of the vectors that are toward the center of the circle so that each points tangent to the circle opposite the existing tangent vectors. she should change the direction of the vectors that are toward the center of the circle so that each points away from the center of the circle. she should change the lengths of the vectors that point toward the center so that each is the same length.

Explanation:

In uniform circular motion, the centripetal force (and thus the centripetal acceleration vector pointing toward the center) has a constant magnitude (since speed is constant and radius is constant, as \(a_c=\frac{v^2}{r}\), and \(v\) and \(r\) are constant). The tangential velocity vectors should also have constant length (constant speed). The vectors toward the center represent centripetal acceleration (or force) and in uniform circular motion, their magnitudes are equal (same \(v\), same \(r\)). So to show uniform circular motion, the lengths of the centripetal (toward - center) vectors should be equal. The other options are incorrect: changing the length of tangential vectors to match centripetal is wrong (they represent different quantities), changing centripetal vectors to tangential or outward is against the definition of uniform circular motion (centripetal acceleration/force must point toward the center).

Answer:

D. She should change the lengths of the vectors that point toward the center so that each is the same length.