F=ma 2025 Problem 09

Physics · mechanics

Problem

Question:

N

circles in a plane,

C_{i}

, each rotate with frequency

\omega

relative to an inertial frame. The center of

C_{1}

is fixed in the inertial frame, and the center of

C_{i}

is fixed on

C_{i - 1}

(for

i = 2, \ldots, N

), as shown in the figure. Each circle has radius

{r}_{i} = \lambda {r}_{i - 1}

, where

0 < \lambda < 1

. A mass is fixed on

C_{N}

. The position of the mass relative to the center of

C_{1}

R\left( t\right)

. For the

N = 4

case shown, which of the following statements is true? During the time interval from 0 to

{2\pi}/\omega

, the magnitude of acceleration of mass on

C_{4}

: (A) reached its maximum and minimum more than once. (B) reached its maximum and minimum exactly once. (C) reached its maximum only once but the minimum more than once. (D) reached its minimum only once but the maximum more than once. (E) was constant. *Note: This problem references figure(s): `image_question/F=MA_2025_09_1.png`*

Browse the problem library