Question

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find the magnitude of the centripetal acceleration of a particle on the tip of a fan blade 0.30 in diameter rotation meaning at 1200 minute ​

Answer 1

Answer:

The length or the circumference of the rotation for one revolution.

1 revolution = πD

= 3.142 × 0.3 = 0.9426 m

How many revolutions does it make per second?

1minute = 60seconds

Revolutions per second is :

1200/60 = 20 revolutions per second.

The length covered in a second is :

20 × 0.9426 = 18.852 m/s

This is the linear velocity.

The centripetal acceleration equals to :

A = V²/r

r = 0.3 / 2 = 0.15m

18.852² / 0.15 = 2369.32 m/s²

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Answer 2

Here, v= 1200/60 =20rps

$w = 2\pi \: v = 2\pi \times 20 = 40\pi \: rad \: s^{2}$

$ac = rw^{2} = 0.15 \times (40\pi)^{2} = 2368.8 \: ms ^{ - 2}$