A point on the edge of a flywheel with a radius of $14 \mathrm{~cm}$ is rotating at a rate of 12 radians per second. What is the linear speed of a point on its rim, in centimeters per minute? The linear speed is approximately $\mathrm{cm} / \mathrm{min}$. (Round to the nearest integer as needed.)

Step 1 ：Given that the radius of the flywheel, \(r\), is 14 cm and the angular speed, \(\omega\), is 12 radians per second.

Step 2 ：The linear speed, \(v\), of a point on the rim of a rotating object is given by the formula \(v = r\omega\). Substituting the given values, we get \(v = 14 \times 12 = 168\) cm/sec.

Step 3 ：We need to convert the linear speed from cm/sec to cm/min by multiplying by 60. So, \(v_{min} = 168 \times 60 = 10080\) cm/min.

Step 4 ：Final Answer: The linear speed of a point on the rim of the flywheel is approximately \(\boxed{10080}\) cm/min.