5 - Circular Motion and Gravitation Free Online FlashCards

Why does constant-speed circular motion involve acceleration?

Yes. Its velocity changes direction continuously, so its acceleration points inward even though its speed remains constant.

What is the direction of tangential velocity?

The instantaneous velocity is tangent to the circular path and perpendicular to the radius from the center to the object.

Is centripetal force a separate physical interaction?

No. Centripetal force is the net inward radial force, which may be supplied by tension, friction, gravity, the normal force, or combinations of these.

What is the period of circular motion?

The period, $T$, is the time required for one complete revolution.

What equations relate angular speed, frequency, and period?

Angular speed is related to frequency by $\omega=2\pi f$, or to period by $\omega=\frac{2\pi}{T}$.

How are circular-path speed, radius, period, and frequency related?

For uniform circular motion, the speed is $v=\frac{2\pi r}{T}=2\pi rf$.

What accelerations occur in nonuniform circular motion?

It has both radial and tangential acceleration: $\vec a=\vec a_c+\vec a_t$. The tangential component changes speed, while the radial component changes direction.

What is the maximum speed on a level curve?

The maximum speed is $v_{\max}=\sqrt{\mu_sgr}$. It does not depend on the car’s mass.

What determines the ideal banking angle?

For an ideal banked curve without friction, $\tan\theta=\frac{v^2}{rg}$, so $\theta=\tan^{-1}\left(\frac{v^2}{rg}\right)$.

Which part of tension turns a conical pendulum?

In a conical pendulum, $T\cos\theta=mg$ vertically and $T\sin\theta$ supplies the inward radial force.

How do radial equations differ at the top and bottom of a loop?

At the top, both forces can point inward, so $N+mg=m\frac{v^2}{r}$. At the bottom, gravity points outward, so $N-mg=m\frac{v^2}{r}$.

What is Newton’s law of universal gravitation?

Newton’s law of universal gravitation is $F_g=G\frac{m_1m_2}{r^2}$. The force is attractive and acts along the line between the centers of mass.