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