The blades of a fan running at low speed turn at 260 RPM. When the fan is switched to high speed, the rotation rate increases uniformly to 380 rpm in 5.30 s. What is the angular displacement, in Radia

The angular displacement (in radians) of the blades can be found using the formula: ? = ?i*t + 1/2*?*t^2, where ? is the angular displacement, ?i is the initial angular velocity, ? is the angular acceleration, and t is the time interval. In this case, the initial angular velocity of the blades is: ?i = 260 RPM = 27.17 rad/s The final angular velocity of the blades is: ?f = 380 RPM = 39.71 rad/s The time interval is: t = 5.30 s The angular acceleration (?) can be found using the equation: ? = (?f - ?i) / t ? = (39.71 - 27.17) / 5.30 ? = 2.372 rad/s^2 Now we can use the formula above to find the angular displacement: ? = ?i*t + 1/2*?*t^2 ? = 27.17*5.30 + 1/2*2.372*5.30^2 ? = 74.09 radians Therefore, the angular displacement of the blades during that time interval is 74.09 radians.