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 acceleration (represented by vectors toward the center in a motion - map) has a constant magnitude. So, the lengths of the vectors pointing toward the center should be the same.

• The first option is incorrect because the tangent vectors (velocity vectors) and centripetal acceleration vectors have different physical meanings and magnitudes (in general, \(a = \frac{v^{2}}{r}\), and they are not equal in length).
• The second option is wrong because changing the direction of the centripetal acceleration vectors (which should point toward the center for centripetal acceleration) to tangent would not represent centripetal acceleration.
• The third option is incorrect as centripetal acceleration is directed toward the center, not away from it.

Answer:

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