# Question #27b73

Jul 16, 2016

#### Answer:

(a) $40 \pi \text{ cm}$
(b) $2.34 \times {10}^{3} c m \cdot {s}^{-} 1$, rounded to two decimal places.
(c) $117.29 r a \mathrm{di} a n \cdot {s}^{-} 1$, rounded to two decimal places.
(d) $0.05 s$, rounded to two decimal places.

#### Explanation:

(a) The tip of fan moves distance equal to one circumference of the circle made by the tip.

$\therefore$ Distance moved by the tip in one revolution$= 2 \pi r$
$= 2 \times \pi \times 20.0 = 40 \pi \text{ cm}$
(d) Time period $T$ of motion is time taken for one revolution.

$\therefore$ Fan makes $1120 r p m$
$\implies T = \frac{60}{1120} = 0.05 s$, rounded to two decimal places.
(c) Angular acceleration $\omega = \frac{2 \pi}{T} = 117.29 r a \mathrm{di} a n \cdot {s}^{-} 1$, rounded to two decimal places.
(b) For circular motion, tip's speed $v = r \omega$
$\implies v = 20.0 \times 117.29 = 2345.72 c m \cdot {s}^{-} 1$