Chap 06 Solutions-1 copy

Chap 06 Solutions-1 copy - ! CIRCULAR MOTION, ORBITS, AND...

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6-1 C IRCULAR M OTION , O RBITS , AND G RAVITY 6 Q6.1. Reason: Looking down from above the player runs around the bases in a counterclockwise direction, hence the angular velocity is positive. Assess: Note that looking from below (from under the grass) the motion would be clockwise and the angular velocity would be negative. We assumed the bird’s eye view because it is standard to do so, and it is difficult to view the game from below the ground. This is akin to setting up a coordinate system with the positive x -axis pointing left and the positive y -axis pointing down; the real-life physics wouldn’t change any, and the calculations of measurable quantities would produce the same results, and it might even be occasionally convenient. But unless there is a clear reason to do otherwise, the usual conventions should be your first thought. Q6.2. Reason: The earth rotates such that the sun rises in the east. A diagram of the sun-earth system as seen from above the north pole follows. The North Pole is represented as the point at the center of the circle in the figure. The directions of east and west are indicated for a person standing at the equator. The person at this position would be seeing the sun just above the horizon in the east. In order for the sun to rise in the east, the earth must be rotating counterclockwise as seen from above the north pole. A point on the earth’s equator would have a positive angular velocity as seen from this position. Assess: Angular velocity is positive for counterclockwise rotations. Q6.3. R e a s on : Acceleration is a change in velocity . Since velocity is a vector, it can change by changing direction, even while the magnitude (speed) remains constant. The cyclist’s acceleration is not zero in uniform circular motion. She has a centripetal (center-seeking) acceleration. Assess: In everyday usage, acceleration usually means only a change in speed (specifically a speeding up), hence the confusion. But in physics we must use words very carefully to communicate clearly. Everyday usage is fine outside the physics context, but while doing physics we must use the precise physics definitions of the words. Q6.4. Reason: In un i fo rm c i r cu l a r mo t ion , th e sp e ed o f an ob j e c t is constant. This is the definition of uniform circular motion in Section 6.1. The direction of the instantaneous velocity is always changing, as illustrated in Figure 6.1. The velocity of an object in uniform circular motion is not constant. The angular velocity for uniform circular motion is given by Equation 6.7, ! = v / r . Since the radius does not change and the speed is constant, the angular velocity of an object in uniform circular motion is constant. The magnitude of the centripetal acceleration of an object in uniform circular motion is given by Equation 6.8, a = v 2 / r .
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Chap 06 Solutions-1 copy - ! CIRCULAR MOTION, ORBITS, AND...

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