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Unformatted text preview: Print this page PROBLEMS sec. 10-2 The Rotational Variables 1 A good baseball pitcher can throw a baseball toward home plate at 85 mi/h with a spin of 1800 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 ft path is a straight line. Answer: 14 rev 2 What is the angular speed of (a) the second hand, (b) the minute hand, and (c) the hour hand of a smoothly running analog watch? Answer in radians per second. 3 When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm and for rotation less than 1 rev, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down? Answer: (a) 4.0 rad/s; (b) 11.9 rad/s 4 The angular position of a point on a rotating wheel is given by = 2.0 + 4.0 t 2 + 2.0 t 3 , where is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.0 s? (d) Calculate its angular acceleration at t = 2.0 s. (e) Is its angular acceleration constant? 5 A diver makes 2.5 revolutions on the way from a 10-m-high platform to the water. Assuming zero initial vertical velocity, find the average angular velocity during the dive. Answer: 11 rad/s 6 The angular position of a point on the rim of a rotating wheel is given by = 4.0 t- 3.0 t 2 + t 3 , where is in radians and t is in seconds. What are the angular velocities at (a) t = 2.0 s and (b) t = 4.0 s? (c) What is the average angular acceleration for the time interval that begins at t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval? 7 The wheel in Fig. 10-27 has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s. You want to shoot a 20 cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. (a) What minimum speed must the arrow have? (b) Does it matter where between the axle and rim of the wheel you aim? If so, what is the best location? Figure 10-27 Problem 7. Page 1 of 20 Problems 12/23/2010 http://edugen.wiley.com/edugen/courses/crs4957/halliday9118/halliday9118c10/aGFsbGl... Answer: (a) 4.0 m/s; (b) no 8 The angular acceleration of a wheel is = 6.0 t 4- 4.0 t 2 , with in radians per second-squared and t in seconds. At time t = 0, the wheel has an angular velocity of +2.0 rad/s and an angular position of +1.0 rad. Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s)....
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This note was uploaded on 01/12/2012 for the course PHYSICS phy 280 taught by Professor Griffo during the Fall '07 term at Bergen Community College.
- Fall '07