Chapter 8

Part 1 of 1

Example Problems & Solutions(useful for homework)

3

• 3. A pitcher throws a curveball that reaches the catcher in 0.6 s. The ball curves because it is spinning at an average angular velocity of 330 rev/min (assumed constant) on its way to the catcher’s mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher ?

13• 13. The drawing (page 242, problem 13 of your

textbook) shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d=0.85 m, and rotating with an angular speed of 95.0 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is theta=0.24 rad. From these data, determine the speed of the bullet.

17

• 17. The drill bit of a variable-speed electric drill has a constant angular acceleration of 2.5 rad/s2. The initial angular speed of the bit is 5.00 rad/s. After 4.0 seconds, (a) what angle has the bit turned through, and (b) what is the bit’s angular speed ?

25• 25. A spinning wheel on a fireworks display is

initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.0 rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0 rad/s. While this change occurs, the angular displacement of the wheel is zero. (Note the similarity to that of a ball being thrown vertically upward, coming to a momentary halt, and then falling downward to its initial position.) Find the time required for the change in the angular velocity to occur.

29

• 29. A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon string that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 47 rev/s, and its tip has a tangential speed of 54 m/s. What is the length of the rotating string ?

35

• 35. A person lowers a bucket into a well by turning the hand crank, as the drawing (page 244, problem 35 in your textbook) illustrates. The crank handle moves with a constant tangential speed of 1.2 m/s on its circular path. Find the linear speed with which the bucket moves down the well.

39

• 39. A race car travels with a constant tangential speed of 75 m.s around a circular track of radius 625 m. Find (a) the magnitude of the car’s total acceleration and (b) the direction of its total acceleration relative to the radial direction.

45

• 45. An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is twice the magnitude of the tangential acceleration. What is the angle ?

47

• 47. A motorcycle accelerates uniformly from rest and reaches a linear speed of 22 m/s in a time of 9 seconds. The radius of each tire is 0.28 m. What is the magnitude of the angular acceleration of each tires ?

55• 55. Consult Concept-Simulation 8.1 at

www.wiley.com/college/cutnell for help in understanding the concepts that are important to this problem. Take two quarters and lay them on a table. Press down on one quarter so it cannot move. Then, starting at the 12:00 position, roll the other quarter along the edge of the stationary quarter, as the drawing (page 245, problem 55 in your textbook) suggests. How many revolutions does the rolling quarter make when it travels once around the circumference of the stationary quarter ? Surprisingly the answer is not one revolution. (Hint: Review the paragraph just before Equation 8.12 that discusses how the distance trveled by the axle of a wheel is related to the circular arc length along the outer edge of the wheel.)