Exercises

1. An apple is cut into nine equal parts. What angle (in radians) is included between the sides of each piece?

2. How many radians does the second hand of a clock turn 30 s? In 90 s? Express your answer in terms of pi.

3. The resolution of the human eye is about 1’, where 60’= 1°. (a) Express an angle of 1’ in radians (b) What is the length of the smallest detail that can be discerned when an object 25 cm away is being examined? ( This is the distance of most distinct vision)

Angular speed

4. What is the angular speed in radians per second of the hour, minute, and second hands of the clock?

5. In 1976, Kazuya Shiozuka made 49,299 turns in 5 h 37 min of skipping rope. Find the average angular speed of the rope.

6. The shaft of a motor rotates at the constant angular speed of 3000 rpm. How many radians will it have turned through in 10 s?

7. In 1941, a wind- driven electric power station was set up at Granpa’s Knob, Vermont. The propeller was 40 m in diameter. When the propeller was turning 30 rev/min, what was the linear speed of one of the blade tips in kilometers per hour?

8. A rotating platform is to be used to test aircraft equipment under acceleration of 6g. If the equipment is 50 cm from the axis, What angular speed is needed?

thx 2 viennah

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