Name:____________________________Date:____________________________ Trigonometry 1.1 Arc Length and Angular Velocity Word Problems 1. A propeller on a plane makes ½ revolution about the axis. Find, in radians, the angular displacement of a point at the tip of the propeller. 2. During the interval t = 2 seconds, the angular displacement of a point P of an object in rotary motion is = 1.64 radians. Find the angular velocity in radians per second. 3. A record player turntable rotates at 33 1/3 revolutions per minute (rpms). Find the angular velocity of the turntable in radians per second. 4. Point P is on the circumference of a phonograph record which is on a turntable rotating at 33 1/3 rpm. Find the angular displacement in radians of point P during ½ second. Find the distance in centimeters to the nearest tenth traveled by point P is the diameter of the record is 30.48 cm. 5. A wheel turns at 600 rad/sec. Find its angular velocity in rpm. 6. The two bladed aircraft propeller is 3.1 meters long. It rotates at 1500 rpm. Find its angular velocity in rad/sec. Find the velocity in m/sec of the tip of a blade as it moves along a circular path. 7. A seat attached to the rim of a ferris wheel at a point P that is 7.6 meters from the axle. The ferris wheel makes one complete revolution every 20 seconds. Find, in m/sec, the velocity of point P along its circular path. 8. A small pulley is connected to a larger pulley by a belt. The crankshaft is turning at 3600 rpm. Find the angular velocity in rad/sec of the large pulley. Find the velocity in cm/sec of point P. Find the velocity in cm/sec of point Q on the belt. Find the angular velocity in rad/sec of the small pulley P . 25 cm r = 2.5 cm 12.5 cm crankshaft Q 9. The small gear in the figure below is turned by an electric motor at 1800 rpm. Find the angular velocity in rad/sec of the small gear. Find the velocity in cm/sec of point P along the circumference of the small gar. Find the angular velociy in rad/sec of the large gear. Find the velocity in cm/sec of point Q along the circumference of the large gear. Q 35 cm P 7 cm 10. The Earth’s axis is the line determined by the north and south poles. Assume that the Earth is a sphere with radius 6336 kilometers that rotates about its axis once in 24 hours. Find, in kilometers per hour, the velocity of a point on the equator as it moves along its circular path. Answers: 1. rad. 2. .82 rad/sec 3. 10/9 rad/sec 4. 5/9 rad/ half sec. 127 /15 cm/half sec. 1800 5. /π rpm 6. 50π rad/sec 155 /2 m/sec 19 7. /25 m/sec 8. 24π rad/sec 600π cm/sec 300π cm/sec 120π rad/sec 9. 60π rad/sec 420π cm/sec 12π rad/sec 420π cm/sec 10. 528π km/hr