Cooling Fan for Electronics
The small fan spins at 1800 rpm and cools a rack of electronic circuit boards (See Figure 8.6). (a) Express the motor’s angular velocity in the units of deg/s and rad/s. (b) Determine the velocity of the 4-cm tip of the fan blade.
Approach
The conversion factors between different dimensions for angular velocity are listed in Table 8.1,
Table 8.1
Conversion Factors between Various Units for Angular Velocity
| rpm | rps | deg/s | rad/s |
| 1 | 1.667×10^{-2} | 6 | 0.1047 |
| 60 | 1 | 360 | 6.283 |
| 0.1667 | 2.777×10^{-3} | 1 | 1.745×10^{-2} |
| 9.549 | 0.1592 | 57.30 | 1 |
and we see from the first row that 1 rpm = 6 deg/s = 0.1047 rad/s. In part (b), the velocity of the fan blade’s tip is perpendicular to the line from the tip to the shaft’s center (Figure 8.7). The velocity is calculated by applying Equation (8.2)
v=rω (8.2)
with angular velocity in the consistent dimensions of rad/s.
