1. Find the angular speeds of the following: (a) Earth's rotation about its axis. (b) The moon's rotation about the earth. (c) The second hand of an analogue clock. 2. A wheel rotating about a fixed axis has an angular position given by off) - 3.0 - 2.0/', where O is measured in radians and / in seconds. What is the angular acceleration of the wheel at / = 2.0 s? 3. A bicycle is moving at a speed of 8.0 m/s. The diameter of each wheel is 70.0 cm. (a) What is the angular velocity (@) of each wheel? (b) If the bicycle is then brought to rest over a distance of 110 m, how many revolutions will each wheel have turned through? 4. The turntable of a record player has an angular velocity of 8.0 rad's when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration. 5. A racecar driver is racing around a circular track with a radius of 500 m. He starts from rest and accelerates uniformly so that in twenty seconds, he has traveled one-fourth of the way around the circle. What is his angular acceleration (a)?6. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel? 7. A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s' starts from rest at = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at : = 0.60 s? 8 . A 10-kg hollow cylindrical shell 50 cm in length and 30 cm in diameter rolls on the ground at a linear velocity of 5 m/s. Find its total kinetic energy. 9. The rotating discs (I = 1%Mr ) shown below have equal mass. Rank in order, from the largest to the smallest, their rotational kinetic energies K., KA K.. (A)K. >K>K. Ko>K. >K. (B)K. >K.>K. (C)K. >K.=K. (D) K. =Ka>K. 10. A uniform solid sphere of radius R and mass M (ICM = 2/5 MR?) rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. Determine the moment of inertia of the sphere about this axis