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flyingcerberus1408
05.10.2019 •
Physics
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.
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Ответ:
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
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)![2.25 m/s^2](/tpl/images/0288/4445/92eaf.png)
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)![3.6 m/s^2](/tpl/images/0288/4445/54c7f.png)
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
Ответ:
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