MATH 122/126: ANGLE AND RADIAN MEASURE

Find the missing part of r, s, t where t is the central angle in a circle of radius r and s is the corresponding arc.

1. r = 4 ft., s = 2 ft.
2. t = $\frac{2}{3}$ radians, r = 3 ft.
3. 3.  t = 60° , s = 9"
4. 4.  r = 3", t = 3 radians

5.  The minute hand of a clock is 2 ft. long. How many inches does its free end move in 20 minutes?

6.  On a circle of radius 50", tangents are drawn at 2 points separated by an arc of length 25". Find the angle between the two tangents.

7.  A car is traveling with a speed of 30 mph. The tread diameter of its tires is 27". Find the speed of rotation of its tires in radians per second; in revolutions per second.

8.  A wheel 6 ft. in diameter is rotating with a uniform angular speed of $1\frac{1}{2}$ radians per second. Find the linear speed of a point on its rim.

9.  A car is traveling at a speed of 45 mph. Find the angular speed of its wheel in radians per second if the diameter is 2.5 ft.

10.  What is the Earth's angular speed in degrees per hour? What has this to do with time zones?

11.  A conveyor belt runs over a pulley at a rate of 40 feet per minute. The radius of the pulley is 2 ft. Find the angular speed of the pulley.

12.  A conveyor belt runs over a pulley at a rate of 10 meters per minute. The pulley is moving at 7 revolutions per minute. Find the radius of the pulley.

1. $\frac{1}{2}$ radians
2. 2 ft.
3. $\frac{27}{\pi }$ in.
4. 9 in.
5. 4.19 ft.
6. $\pi -\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ radians
7. $\frac{352}{9}=39.\overline{1}$ radians/sec, $\frac{176}{9\pi }\approx 6.22$ rev/sec
8. $4\frac{1}{2}$ ft./sec.
9. $\frac{264}{5}$ radians/sec or 52.8 radians/sec
10. 15° per hour;
    15° makes 1 hour difference
11. 20 radians/min.
12. $\frac{5}{7\pi }$ meters