Chapter 16 Practice
1
The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour.
(a) Through how many radians does it turn in 100 minutes?
(b) How long does it take the restaurant to rotate through 4 radians?
(c) How far does a person sitting by the window move in 100 minutes if the radius of the
restaurant is 21 meters?
2.
Answer the following angular speed questions.
(a) A wheel of radius 22 ft. is rotating 11 RPM (revolutions per minute) counterclockwise.
Considering a point on the rim of the rotating wheel, what is the angular speed ω in
rad/sec and the linear speed v in ft/sec?
(b) A wheel of radius 8 in. is rotating 15 degrees/sec. What is the linear speed v, the
angular speed in RPM and the angular speed in rad/sec?
(c) You are standing on the equator of the earth (radius 3960 miles). What is your linear
and angular speed?
(d) An auto tire has radius 12 inches. If you are driving 65 mph, what is the angular speed
in rad/sec and the angular speed in RPM?
3.
Lee is running around the perimeter of a circular track at a rate of 10 ft/sec. The track has a
radius of 100 yards. After 10 seconds, Lee turns and runs along a radial line (a radius) to the
center of the circle. Once he reaches the center, he turns and runs along a radial line to his
starting point on the perimeter.
Assume Lee does not slow down when he makes these two turns.
(a) Sketch a picture of the situation.
(b) How far has Lee traveled once he returns to his starting position?
(c) How much time will elapse during Lee’s circuit?
(d) Find the area of the pie shaped sector enclosed by Lee’s path.
Continues next page…
1
The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour.
(a) Through how many radians does it turn in 100 minutes?
(b) How long does it take the restaurant to rotate through 4 radians?
(c) How far does a person sitting by the window move in 100 minutes if the radius of the
restaurant is 21 meters?
2.
Answer the following angular speed questions.
(a) A wheel of radius 22 ft. is rotating 11 RPM (revolutions per minute) counterclockwise.
Considering a point on the rim of the rotating wheel, what is the angular speed ω in
rad/sec and the linear speed v in ft/sec?
(b) A wheel of radius 8 in. is rotating 15 degrees/sec. What is the linear speed v, the
angular speed in RPM and the angular speed in rad/sec?
(c) You are standing on the equator of the earth (radius 3960 miles). What is your linear
and angular speed?
(d) An auto tire has radius 12 inches. If you are driving 65 mph, what is the angular speed
in rad/sec and the angular speed in RPM?
3.
Lee is running around the perimeter of a circular track at a rate of 10 ft/sec. The track has a
radius of 100 yards. After 10 seconds, Lee turns and runs along a radial line (a radius) to the
center of the circle. Once he reaches the center, he turns and runs along a radial line to his
starting point on the perimeter.
Assume Lee does not slow down when he makes these two turns.
(a) Sketch a picture of the situation.
(b) How far has Lee traveled once he returns to his starting position?
(c) How much time will elapse during Lee’s circuit?
(d) Find the area of the pie shaped sector enclosed by Lee’s path.
Continues next page…
