Student Guide: Circular Motion

Fill-in-the-blank practice cards covering key concepts, formulas, worked examples, and practice problems from the Circular Motion student guide.

The center-seeking acceleration directed inward toward the center of a circular path, which is responsible for changing the direction of velocity, is called __________ acceleration.

centripetal

In uniform circular motion, an object travels at a constant speed, but acceleration is always present because velocity is a vector and its __________ is continuously changing.

direction

Centripetal force is not a distinct physical force on its own; rather, it is the __________ required to keep an object on a circular path.

net force

The real physical force that provides the necessary centripetal force to keep satellites and planets in orbital motion is __________.

gravity

If an object changes speed while moving along a circular path, it experiences centripetal acceleration ($a_c$) pointing toward the center and __________ acceleration ($a_t = \frac{dv}{dt}$) pointing along the path.

tangential

In terms of angular speed ($\omega$) and radius ($r$), centripetal acceleration is expressed by the formula $a_c =$ __________.

$$\omega^2 r$$

For a satellite orbiting a planet at a radius of $r = 7{,}000{,}000\,m$ with an orbital speed of $v = 3{,}000\,m/s$, the calculated centripetal acceleration ($a_c$) is approximately __________.

$$1.29\,m/s^2$$

A carousel with radius $r = 4\,m$ that completes $2$ full revolutions ($4\pi\text{ radians}$) every $5\text{ seconds}$ has an angular speed ($\omega$) of approximately __________.

$$2.51\,rad/s$$

If you double the tangential speed $v$ of a car rounding a curve of fixed radius $r$, the required centripetal force __________ because $F_c \propto v^2$.

quadruples (4x)

A rotating wheel takes $0.5\,s$ to complete one full revolution; using $f = \frac{1}{T}$, its rotation frequency is __________.

$$2.0\,Hz$$