1. A fan blade rotates with angular velocity given by z(t)= t^2. a) Calculate the angular acceleration as a function of time. Express your answer in terms of the variables , , and t . b)If = 5.50 rad/s and = 0.830 rad/s3 , calculate the instantaneous angular acceleration z at t = 3.10 s. Express your answer in radians per second squared. c) If = 5.50 rad/s and = 0.830 rad/s3 , calculate the average angular acceleration avz for the time interval t = 0 to t = 3.10 s. Express your answer in radians per second squared.

2. A wheel is rotating about an axis that is in the z-direction. The angular velocity z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 10.0s. We have taken counterclockwise rotation to be positive. a) Is the angular acceleration during this time interval positive or negative? positive or negative? b) How long is the time interval during which the speed of the wheel is increasing? Express your answer with the appropriate units. c) How long is the time interval during which the speed of the wheel is decreasing? Express your answer with the appropriate units. d) What is the angular displacement of the wheel from t = 0s to t = 10.0s ? Express your answer in radians.

3. A wheel rotates from rest with constant angular acceleration. a) If it rotates through 8.00 revolutions in the first 2.50s , how many more revolutions will it rotate through in the next 5.00? Express your answer in revolutions.

4. At t = 0 a grinding wheel has an angular velocity of 20.0 rad/s. It has a constant angular acceleration of 27.0 rad/s2 until a circuit breaker trips at time t = 1.90s. From then on, it turns through an angle 434 rad as it coasts to a stop at constant angular acceleration. a) Through what total angle did the wheel turn between t = 0 and the time it stopped? Express your answer in radians. b) At what time did it stop? Express your answer in seconds. c) What was its acceleration as it slowed down? Express your answer in radians per second squared.