Question

consider two objects: one moves in a circle with a large radius, and the other moves in a circle with a small radius. if both objects are moving at the same speed, which object experiences the greater centripetal acceleration?
a) the object with the larger radius
b) both objects experience the same centripetal acceleration
c) the object with the smaller radius
d) the object with the greater speed experiences the greater centripetal acceleration

Explanation:

Step1: Recall centripetal acceleration formula

The formula for centripetal acceleration is \(a_c=\frac{v^2}{r}\), where \(v\) is the speed and \(r\) is the radius of the circular path.

Step2: Analyze the relationship between \(a_c\) and \(r\) for constant \(v\)

Given that \(v\) is the same for both objects. Let \(a_{c1}=\frac{v^2}{r_1}\) and \(a_{c2}=\frac{v^2}{r_2}\). If \(r_1 > r_2\) (where \(r_1\) is the large - radius and \(r_2\) is the small - radius), then \(\frac{v^2}{r_1}<\frac{v^2}{r_2}\) (since when the numerator \(v^2\) is constant, and the denominator \(r\) decreases, the value of the fraction increases).

Answer:

C. The object with the smaller radius