Chapter 6, Problem 1CQ

There an analogy between rotational and physical quantities. What rotational quantities are analogous to distance and velocity?

To determine

The rotational quantities which are analogues to distance and velocity

Answer to Problem 1CQ

The rotational quantities which are analogues to distance and velocity are rotation angle and angular velocity respectively.

Explanation of Solution

The rotation angle is the amount of rotation of an object it is analogues to linear distance. It is defined as the ratio of arc length and radius of curvature

$\Delta \theta =\frac{\Delta s}{r}$

Here,

$\Delta s$ is arc length

$r$ is radius of curvature

The angular velocity defines how fast an object is rotating about a point it is analogues to the linear velocity. It is defined as the rate of change of rotation angle

$\omega =\frac{\Delta \theta }{t}$

Here,

$\Delta \theta$ is the rotation angle

$t$ is time

Conclusion:

The rotational quantities which are analogues to distance and velocity are rotation angle and angular velocity respectively.