An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.300 rev/s . the magnitude of the angular acceleration is 0.895 rev/s^2 . both the the angular velocity and angular accleration are directed counterclockwise. the electric ceiling fan blades form a circle of diameter 0.800 m . question1- what is the tangential speed vt of a point on the tip of the blade at time t = 0.200 s ?
question 2- calculate the magnitude at of the tangential acceleration of a point on the tip of the blade at time t = 0.200 s .
question 3- calculate the magnitude ar of the radial (or centripetal) acceleration of the point at the end of the fan blade.

1) 1.2 m/s

First of all, we need to find the angular velocity of the blade at time t = 0.200 s. This is given by

where

is the initial angular velocity

is the angular acceleration

Substituting t = 0.200 s, we find

Let's now convert it into rad/s:

The distance of a point on the tip of the blade is equal to the radius of the blade, so half the diameter:

And so now we can find the tangential speed at t = 0.200 s:

2)

The tangential acceleration of a point rotating at a distance r from the centre of the circle is

where is the angular acceleration.

First of all, we need to convert the angular acceleration into rad/s^2:

A point on the tip of the blade has a distance of

r = 0.400 m

From the centre; so, the tangential acceleration is

3)

The centripetal acceleration is given by

where

v is the tangential speed

r is the distance from the centre of the circle

We already calculate the tangential speed at point a):

v = 1.2 m/s

while the distance of a point at the end of the blade from the centre is

r = 0.400 m

Therefore, the centripetal acceleration is

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