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Chap 07 Solutions copy 2

Chap 07 Solutions copy 2 - ROTATIONAL MOTION 7 Q7.1 Reason...

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7-1 R OTATIONAL M OTION 7 Q7.1. Reason: By convention, clockwise rotations are negative and counterclockwise rotations are positive. As a result, an angular acceleration that decreases/increases a negative angular velocity is positive/negative. In like manner, an angular acceleration that decreases/increases a positive angular velocity is negative/positive. Knowing this we can establish the situation for each figure. Figure (a) the pulley is rotating clockwise ( ! = –), however since the large mass is on the left it is decelerating ( " = +). Figure (b) the pulley is rotating counterclockwise ( ! = +) and since the large mass is on the left it is accelerating ( " = +). Figure (c) the pulley is rotating clockwise ( ! = –) and since the large mass is on the right it is accelerating ( " = –). Figure (d) the pulley is rotating counterclockwise ( ! = +), however since the large mass is on the right it is decelerating ( " = –). Assess: It is important to know the sign convention for all physical quantities that are vectors. This is especially important when working with rotational motion. Q7.2. Reason: Since we are dealing with a stubborn nut, we want a large torque. For a given force the torque is increased by increasing the moment arm. Slipping a length of pipe over the wrench handle increases the moment arm and hence the applied torque. Assess: You can increase the torque by either increasing the force or the moment arm. In this case we chose to increase the torque by increasing the moment arm. Q7.3. Reason: The question properly identified where the torques are computed about (the hinge). Torques that tend to make the door rotate counterclockwise in the diagram are positive by convention (general agreement) and torques that tend to make the door rotate clockwise are negative. (a) + (b) # (c) + (d) # (e) 0 Assess: Looking at the diagram we see that F !" a and F !" c are parallel and are both creating a negative or counterclockwise torque. But since F !" c is farther from the hinge, its torque will be greater. A similar argument can be made for F !" b and F !" d . Note that F !" e causes no torque since it has no moment arm. Q7.4. Reason: The screwdriver with a thick handle has a larger radius and so provides a larger moment arm for the force you exert when turning the driver. The larger moment arm leads to a larger torque on the screw. This can be seen from Equation 7.4. Assess: For a given force a larger moment arm leads to a larger torque. Q7.5. Reason: The reason for large-diameter steering wheels in trucks is that more torque is needed to turn the wheels due to the greater mass of the truck. Making the steering wheel larger means that more torque is exerted on the steering shaft for the same force from the driver’s hands. Assess: Most light cars employ a rack-and-pinion steering system, while larger SUVs and trucks often employ a recirculating-ball steering system; however both systems can be assisted by pressurized hydraulic fluid (power steering), so steering, even in trucks, can be much easier than in the old days.
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7-2 Chapter 7 Q7.6.
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