Solving Word Problems Involving Angular Velocity
Solving Problems Involving Angular Velocity
Among the challenging problems I encounter in Trigonometry are problems involving angular velocity. In this hub, I presented several problems involving angular velocity with their solution.
Problem Number One :
A calesa with wheels whose diameter is 1.5 meters is traveling at 24 kph. Find the angular velocity of the wheel in revolutions per minute.
Radius ( r ) = 1.5/2 = .75 m =è .75 (1/1000) = .00075 km
Linear Velocity (V) = 24 kph
Angular Velocity (W) = ? in revolution per minute
V = r W =è W = V/r
W = (24 km/hr )(1/.00075 km) = 32,000 radians per hour
To convert to revolution per minute :
(32,000 rad/hr) (1 rev/2∏) (1 hr/60 min) = 32,000/376.992 = 84.88
Problem Number Two :
A man was jogging on an oval track with radius 89 meters. If the man was jogging at a speed of 25 m/min, what was the central angle generated by the man after 5 minutes ?
Radius ( r ) = 89 m
Linear Velocity ( V ) = 25 m/min
Time ( t ) = 5 minutes
W = ө / t W = V/ r
W = ( 25m/min) ( 1/89m) = 25/89 rad/ min = 0.281 rad/min
ө = Wt
ө = (.281 rad/min) (5 min) - 1.4 radian
Convert 1.4 radian to degrees : ( 1.4 ) ( 180/∏ ) = 80.21 degrees
Problem Number Three :
Suppose a point on a circle with radius 6 cm moves around a circle with angular velocity of 2∏/5 rad/sec. What is the length of the arc generated after 10 seconds ?
Radius ( r ) = 6 cm
Angular Velocity (W ) = 2∏/5 rad/sec
Time ( t ) = 10 seconds
S = ? arc length
V = r W
= (6 cm ) (2) (3.1416)/5 = 7.54 cm/sec
S = Vt
S = ( 7.54 cm/sec) (10 sec) = 75.4 cm
Problem Number Four :
Find the radius of a pulley which is driven at 10 rev/sec by a belt moving at 10m/sec.
W = 10 rev/sec
V = 10 m/sec
Radius ( r ) = ?
R = V/W
W = (10 rev/sec) (2 ∏ rad/rev ) = 20 ∏ rad/sec
r = (10m/sec ) /(20 ∏rad/sec) = 0.16 m
Problem Number Five :
A ferriswheel has a diameter of 10 meters. It is rotating at the rate of 500 m/min. Find its angular velocity in rad/sec.
Radius ( r ) = 10/2 = 5 m
Velocity (V ) = 500 m/min
W = ?
W = V/r
W = (500m/min )/5m = 100 rad/min
= (100 rad/min) (1 min/60 sec) = 100/60 rad/sec = 1.7 rad/sec
Problem Number Six :
Find the linear velocity of the tip of the minute hand of a clock if the hand is 7cm
V = S / t
Radius ( r ) = 7cm
W = 1 rev/hr = 2∏ rad/hr
V = ?
V = r W
V = (7 cm) (2∏rad/hr) = 14 ∏ cm/hr = ( 14∏/60) cm/min = .73 cm/min