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(c) Find the linear velocity of P Ans:  EMBED Equation.DSMT4 cm per second. Example 2: A belt runs a pulley of radius 6 cm at 80 revolutions per minute. (a) Find the angular velocity of the pulley in radians per second. Ans:  EMBED Equation.DSMT4  rad/s (b) Find the linear velocity of the belt in centimeters per second.  EMBED Equation.DSMT4 cm/s. Example 3: A satellite traveling in a circular orbit 1600 km above the surface of Earth takes two hours to make an orbit. Assume that the radius of Earth is 6400 km. (a) Find the linear velocity of the satellite. Ans:  EMBED Equation.DSMT4  km/ hr. (b) Find the distance traveled in 4.5 hours. Ans:  EMBED Equation.DSMT4 km. Exercises: 1. If a point moves around the circumference of a unit circle at an angular velocity of 1 radian per second, how long will it take for the point to move around the entire circle? Ans: 2 EMBED Equation.DSMT4 sec. 2. If a point moves around the circumference of a unit circle at a speed of 2 units per second, how long will it take for the point to move around the entire circle? Ans:  EMBED Equation.DSMT4 sec 3. Find  EMBED Equation.DSMT4  for each of the following. a) The minute hand of a clock b) the second hand of a clock Ans:  EMBED Equation.DSMT4 /30rad/min  EMBED Equation.DSMT4 /30 rad/sec. 4. Find v for the tip of the hour hand of a clock, if the hand is 6cm long. Ans:  EMBED Equation.DSMT4 cm/hr 5. Find v for a point on the edge of a flywheel of radius 2 m, rotating 15 times per minute Ans: 60  EMBED Equation.DSMT4  m/min. 6. Find v for the tip of an airplane propeller 4 m long, rotating 500 times per minute. Ans: 2000  EMBED Equation.DSMT4  m/min. 7. The tires of a bicycle have radius 13 inches and are turning at the rate of 200 revolutions per minute. How fast is the bicycle traveling in miles per hour? (Hint: 5280 feet = 1 mile.) Ans: 15.5mi/h 8. Mars rotates on its axis at the rate of .2552 radians per hour. Approximately how many hours are in a Martian day? Ans: 24.6206hrs. 9. Earth travels about the sun in an orbit that is almost circular. Assume that the orbit is a circle, with radius 93,000,000 miles. Its angular and linear velocities are used in designing solar power facilities. (a) Assume that a year is 365 days, and find EMBED Equation.DSMT4 , the angle formed by Earths movement in one day. Ans:  EMBED Equation.DSMT4 /182.5rad (b) Give the angular velocity in radians per hour. Ans:  EMBED Equation.DSMT4 /4380 rad/hr. (c) Find the linear velocity of Earth in miles per hour. Ans: 66,700 mi/hr. 10. A pulley has a radius of 12.96 cm. Suppose it takes 18 seconds for 56cm of a belt to go around the pulley. Find the angular velocity of the pulley in radians per second. Ans: .24rad/sec. 11. The two pulleys connected by a belt have radii of 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36 seconds. Find the angular velocity of each pulley in radians per second. Ans: large: 25 EMBED Equation.DSMT4 /18; small: 125 EMBED Equation.DSMT4 /48 12. A thread is being pulled off a spool at the rate of 59.4 cm per second. Find the radius of the spool if it makes 152 revolutions per minute. Ans: 3.73cm. 13. Earth revolves on its axis once every 24 hours. Assuming that Earths radius is 6400 km. find the following: (a) angular velocity of Earth in radians per day and radians per hour. Ans:  EMBED Equation.DSMT4 /12rad/hr (h) linear velocity at the North Pole or South Pole. Ans: v= 0 (c) linear velocity at Quito, Ecuador, a city on the equator Ans: 1600 EMBED Equation.DSMT4 /3 km/hr. (d) linear velocity at Salem, Oregon (halfway from the equator to the North Pole) Ans: 800 EMBED Equation.DSMT4 /3 km/hr. 14. A railroad track is laid along the arc of a circle of radius 1800 feet. The circular part of the track subtends a central angle of 40. 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