1- An electric fan is turned off, and its angular velocity decreases uniformly f

ID: 2116986 • Letter: 1

Question

1-An electric fan is turned off, and its angular velocity decreases uniformly from 450

rev/min to 160rev/min in a time interval of length 3.80s .

A-Find the angular acceleration in

rev/s2.

B-Find the number of revolutions made by the motor in the time interval of length 3.80

C-How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part A?

2-A uniform sphere with mass 35.5

kg and radius 0.400m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere.

If the kinetic energy of the sphere is 144J , what is the tangential velocity of a point on the rim of the sphere?

1. u = 450* 2pi/60 rad/sec =47.12 rad/sec

v = 160*2pi/60 rad/sec = 16.755 rad/sec

v=u+at

16.755 = 47.12+a*3.8

solving,

a = -7.99 rad/s^2 --------------ANSWER for part A

s = ut+0.5at^2

s= 47.12*3.8-0.5*7.99*3.8^2 = 121.36 rad =121.36/(2pi) rev = 19.32 revoltions ----part B

v=u+at

0=47.12-7.99*t

t =5.89

already , t is at 3.8 so more (5.89-3.8 = 2.09) sec ----PART C

2. Rotational KE = 1/2 I (V/r)^2 = 144

0.5*(2*35.5*0.4^2/5) *(v^2) = 144*0.4^2

solving, V = 4.5 m/sec -------ANSWER for second part

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