# hw12 - t = 0 s the normal acceleration at the tip of the...

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Homework No. 12 Relating rotational kinematics to translational kinematics P a b υ b CHANG 1 A rotating pulley with radius R = 0.04 m is driven by the belt as shown. If the speed of the belt is 0.2 m/s, and point P on the rim of the pulley has a total acceleration of 2.6 m/s 2 , find the angular acceleration of the pulley. Ans : –60 rad/s 2 O 1 O 2 A B a b b CHANG 2 A belt passes over two pulleys O 1 (radius R 1 = 0.4 m) and O 2 (radius R 2 = 0.6 m) as shown, and points A and B are on the rim of the pulleys. The normal acceleration at A is 0.9 m/s a the angular acceleration of pulley O nd 2 . 1 is 3.6 rad/s Find (a) the belt velocity υ b , (b) the belt acceleration a b , and (c) the acceleration of B . Ans : (a) 0.6 m/s (b) 1.44 m/s 2 (c) 1.56 m/s 2 Combination problems CHANG 3 A spinning blade is 1.2 m long and is pivoted at its center. At
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Unformatted text preview: t = 0 s, the normal acceleration at the tip of the blade is 2.4 m/s 2 . The blade is rotating with a constant angular acceleration, and when t = 5 s the blade rotates through an angle of 110 rad. Find the speed at the tip of the blade at t = 5 s. Ans : 25.2 m/s CHANG 4 At t = 0 s a point P on the rim of the a disk has an initial speed of 50 m/s, and its motion starts to slow down at a constant tangential deceleration of 10 m/s 2 . At what time will the normal acceleration equal g if the diameter of the disk is 0.4 m? Ans : 4.86 s 2.5 m 1 m O 36.87° F 1 = 100 N F 2 = 120 N Torque CHANG 5 Find the total torque about the pivot O by the two forces. Ans : 60 N·m CW...
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