$A C D$ has a diameter of $12.0 \mathrm{~cm}$. If the $C D$ is rotating at a constant angular speed of 200 revolutions per minute, then the linear speed of a point on the circumference is Multiple Choice $106 \mathrm{~m} / \mathrm{s}$. $1.26 \mathrm{~m} / \mathrm{s}$ $1.39 \mathrm{~m} / \mathrm{s}$. $1.62 \mathrm{~m} / \mathrm{s}$ $1.32 \mathrm{~m} / \mathrm{s}$.

Step 1 ：The diameter of the circle $ACD$ is given as 12.0 cm. Therefore, the radius $r$ of the circle is half of the diameter, which is \(r = \frac{12.0}{2} = 6.0\) cm or 0.06 m.

Step 2 ：The angular speed is given as 200 revolutions per minute. We need to convert this to radians per second. Since there are \(2\pi\) radians in one revolution and 60 seconds in one minute, the angular speed \(\omega\) is \(\omega = \frac{200 \times 2\pi}{60}\) radians per second.

Step 3 ：The linear speed $v$ of a point on the circumference of a circle is given by the formula $v = r\omega$. Substituting the values of $r$ and $\omega$ we get, $v = 0.06 \times 20.943951023931955 = 1.2566370614359172$ m/s.

Step 4 ：Rounding off the above value to two decimal places, we get the linear speed as $v = 1.26$ m/s.

Step 5 ：\(\boxed{1.26 \mathrm{~m} / \mathrm{s}}\) is the final answer.