Question

Lucia wants to change the motion map shown so that it shows uniform circular motion. an illustration of a circle with four black dots on the top, bottom, left and right of the circle. each dot has a vector toward the center of the circle and a vector tangent to the circle in a counterclockwise direction. what change should lucia make? a. 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. b.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. c.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.

Answer 1

Lucia does not need to make any changes to her motion map as it already correctly represents uniform circular motion with vectors for centripetal acceleration pointing toward the center and equal-length tangent velocity vectors.

Step-by-step explanation:

To show uniform circular motion, Lucia needs to ensure that both the centripetal acceleration and the tangential velocity vectors are properly represented. Centripetal acceleration points toward the center of the circular path, which she already has in her illustration. However, for uniform circular motion, the speed of the particle is constant, and thus the tangential velocity vectors, which are tangent to the circle, must also be of constant magnitude throughout the motion. Therefore, the lengths of the velocity vectors should remain the same at all points on the circle, depicting a uniform speed. In uniform circular motion, the centripetal acceleration can be described as = v² /r, where 'v' is the constant speed and 'r' is the radius of the circle.

As for the correct answer to the question: Lucia should not change the lengths of the centripetal acceleration vectors that point toward the center since the particle's speed is constant in uniform circular motion, nor should she change their direction. Her vectors are already correctly showing both the radial and tangential components of the motion in a scenario of uniform circular motion. Therefore, no changes are required to the motion map for it to represent uniform circular motion.