An electric fan has blades of length $30 ext{ cm}$ as measured from the axis of rotation. If the fan is rotat

Question

An electric fan has blades of length $30	ext{ cm}$ as measured from the axis of rotation. If the fan is rotating at $1200	ext{ r.p.m}$, the acceleration of a point on the tip of the blade is about:

Accepted Answer

1.  **Identify Given Values:**
    *   Radius ($R$) = length of blade = $30	ext{ cm} = 0.3	ext{ m}$.
    *   Frequency ($n$) = $1200	ext{ revolutions per minute (r.p.m)}$.
2.  **Convert Units:**
    *   Convert frequency to revolutions per second: $v = \frac{1200}{60} = 20	ext{ rev/s}$.
    *   Calculate angular velocity ($\omega$): $\omega = 2\pi v = 2\pi(20) = 40\pi	ext{ rad/s}$ .
3.  **Calculate Acceleration:**
    The centripetal acceleration ($a_c$) is given by the formula $a_c = \omega^2 R$ .
    $a_c = (40\pi)^2 	imes 0.3$
    $a_c = 1600\pi^2 	imes 0.3$
    $a_c = 480\pi^2$
    Using $\pi^2 \approx 9.87$:
    $a_c \approx 480 	imes 9.87 = 4737.6	ext{ m/s}^2$.
    This value is approximately $4740	ext{ m/s}^2$.

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