*48. At a county fair there is a betting game that involves a spinning wheel.
As the drawing shows, the wheel is set into rotational motion with the begin-
ning of the angular section labeled "1" at the
marker at the top of the wheel. The wheel then
decelerates and eventually comes to a halt on
one of the numbered sections. The wheel
in the drawing is divided into 12 sections,
each of which is an angle of 30.0°. Determine
the numbered section on which the wheel
comes to a halt when the deceleration of the
wheel has a magnitude of 0.200 rev/s² and the
inititial angular velocity is (a) +1.20 rev/s and
*50. An automobile, starting from rest, has a linear acceleration to the right
whose magnitude is 0.800 m/s² (see the figure). During the next 20.0 s, the
tires roll and do not slip. The radius of each wheel is 0.330 m. At the end of
this time, what is the angle through which each wheel has rotated?
*49. A racing car, starting from rest, travels around a circular turn of ra-
dius 23.5 m. At a certain instant, the car is still accelerating, and its an-
gular speed is 0.571 rad/s. At this time, the total acceleration (centripetal
plus tangential) makes an angle of 35.0° with respect to the radius. (The
situation is similar to that in Figure 8.12b.) What is the magnitude of the
total acceleration?
