Question

name:_____________________________ period: ___________
ucm-circular motion

1. the diagram at right shows an object moving counterclockwise around a horizontal,

circular track.
which diagram represents the direction of both the object’s velocity and the centrip-
etal force acting on the object when it is in the position shown?

(1) (2) (3) (4)

1. which graph best represents the relationship between the magnitude of the centripetal acceleration and the

speed of an object moving in a circle of constant radius?

(1) (2) (3) (4)

Explanation:

Step1: Analyze velocity direction

In uniform circular motion, velocity is tangent to the circle. For counterclockwise motion at the rightmost position, velocity points upward.

Step2: Analyze centripetal force direction

Centripetal force always points toward the center of the circle. At the rightmost position, the center is to the left, so force points left.

Step3: Match with diagrams (Q9)

Only diagram (2) has upward velocity and leftward centripetal force.

Step4: Relate centripetal acceleration to speed (Q10)

Centripetal acceleration formula: $a_c = \frac{v^2}{r}$. For constant $r$, $a_c \propto v^2$, which is a quadratic curve starting at the origin. This matches diagram (2).

Answer:

Q9: (2)
Q10: (2)