(Solved): 1, 9 1. Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so t ...

1. Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions-it then calculates the distance traveled. If the wheel has a \( 1.15 \mathrm{~m} \) diameter and goes through 200,000 rotations, how many kilometers should the odometer read? 2. Microwave ovens rotate at a rate of about 6 revimin. What is this in revolutions per second? What is the angular velocity in radians per second? 3. An automobile with \( 0.260 \mathrm{~m} \) radius tires traveis \( 80,000 \mathrm{~km} \) before wearing them out. How many revolutions do the tires make, neglecting any backing up and ary change in radius due to wear? 4. (a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of \( 6.4 \times 10^{6} \mathrm{~m} \) at its equator, what is the linear velocity at Earth's surface? 5. A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher's hand is \( 35.0 \mathrm{~m} / \mathrm{s} \) and the ball is \( 0.300 \mathrm{~m} \) from the elbow joint, what is the angular velocity of the forearm? 6. In tacrosse, a bail is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is \( 30.0 \mathrm{rad} / \mathrm{s} \) and the ball is \( 1.30 \mathrm{~m} \) from the elbow joint, what is the velocity of the ball? 7. A truck with \( 0.420-\mathrm{m}- \) radius tires travels at \( 32.0 \mathrm{~m} / \mathrm{s} \). What is the angular velocity of the rotating tires in radians per second? What is this in revjmin? 8. Integrated Concepts When kicking a football, the kicker rotates his leg about the hip joint. (a) If the velocity of the tip of the kicker's shoe is \( 35.0 \mathrm{~m} / 5 \) and the hip joint is \( 1.05 \mathrm{~m} \) from the tip of the shoe, what is the shoe tip's angular velocity? (b) The shoe is in contact with the initially stationary \( 0.500 \mathrm{~kg} \) football for \( 20.0 \mathrm{~ms} \). What average force is exerted on the football to give it a velocity of \( 20.0 \mathrm{~m} / \mathrm{s} \) ? (c) Find the maximum range of the football, neglecting air resistance. 9. Construct Your Own Problem Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in which you calculate the necessary angular velocity that assures the riders will not slide down the wall, Include a free body diagram of a single rider. Among the variables to consider are the radius of the cylinder and the coefficients of friction between the riders' clothing and the wall,