Chapter 7 Rotational Motion Law of Gravity Quick Quizzes Solutions

(c). For a rotation of more than 180°, the angular displacement must be larger than p = 3.14 rad. The angular displacements in the three choices are (a) 6 rad - 3 rad = 3 rad, (b) 1 rad -(-1) rad = 2 rad, (c) 5 rad -1 rad = 4 rad.

 2.         (b). Because all angular displacements occurred in the same time interval, the displacement with the lowest value will be associated with the lowest average angular speed.

 3.          (b). From
                               
                it is seen that the case with the smallest angular displacement involves the highest angular acceleration.

 4.          (b). All points in a rotating rigid body have the same angular speed.

 5.          (a). Andrea and Chuck have the same angular speed, but Andrea moves in a circle with twice the radius of the circle followed by Chuck. Thus, from , it is seen that Andrea’s tangential speed is twice Chuck’s.

 6.          1. (e). Since the tangential speed is constant, the tangential acceleration is zero.

2. (a). The centripetal acceleration, , is inversely proportional to the radius when the tangential speed is            constant.

               3. (b). The angular speed, , is inversely proportional to the radius when the tangential speed is constant.

 7.        (c). Both the velocity and acceleration are changing in direction, so neither of these vector quantities is constant.

 8.        (b) and (c). According to Newton’s law of universal gravitation, the force between the ball and the Earth depends on the product of their masses, so both forces, that of the ball on the Earth, and that of the Earth on the ball, are equal in magnitude. This follows also, of course, from Newton’s third law. The ball has large motion compared to the Earth because according to Newton’s second law, the force gives a much greater acceleration to the small mass of the ball.

 9.        (e). From F = G Mm/r², the gravitational force is inversely proportional to the square of the radius of the orbit.

10.        (d). The semi-major axis of the asteroid’s orbit is 4 times the size of Earth’s orbit. Thus, Kepler’s third law (T²/r³ = constant) indicates that its orbital period is 8 times that of Earth.