In: Physics
An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.260 rev/s . The magnitude of the angular acceleration is 0.881 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750 m .
What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.203 s ?
What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.203 s ?
initial angular velocity , w0 = 0.260 rev/sec ( w = theta /t, theta = 2*pie --- in 1 rev)
= 0.260*2*pie = 1.632 rad/sec ( pie= 3.14)
@ ( angular acceleration) = 0.881 rev / s2
= 0.881*2*3.14 = 5.53 rad/s2
w ( final angular velocity) = w0 + @ *t
w = 1.632 + 5.53*0.203
w = 2.75 rad/s
a) tangential velocity, Vt = w*r ( r = radius = 0.750/2 m)
= 2.75* 0.750 / 2
= 1.031 m/s
b) resultant acceleration ( aR ) will be the vector sum of centripetal acceleration ( ac ) and tangential acceleration ( at )
ac = w2 * r
= 2.752 * 0.750 / 2
= 2.835 m/s2
at = @*r
= 5.53* 0.750/2
= 2.073 m/s2
aR = ( ac2 + at2 ) 1/2
= 3.51 m/s2