Question

The angular frequency of a fan increases from 30 rpm to 60 rpm in 3.14 sec . a dust particle is present at a distance of 20 cm from axis of rotation. the tangential acceleration of particle in 3.14 sec is

Answer 1

angular frequency of the fan will increase from 30 rpm to 60 rpm in 3.14 s

so angular speed is given by

$\omega_i = 2 \pi \frac{30}{60} = \pi rad/s$

$\omega_f = 2 \pi \frac{60}{60} = 2\pi rad/s$

now angular acceleration is given as

$\alpha = \frac{\omega_f - \omega_i}{t}$

$\alpha = \frac{2\pi - \pi}{3.14}$

$\alpha = 1 rad/s^2$

now the tangential acceleration is given as

$a_t = r* \alpha$

given that

r = 20 cm = 0.20 m

now by the above equation

$a_t = 0.20 * 1 = 0.20 m/s^2$

so the tangential acceleration is 0.20 m/s^2

Answer 2

Answer:

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Explanation: