# 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.

Given :

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 ?

Given :

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 ?

Given :

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.

Given :

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

Long ?

V = S / t

Given :

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

## Comments

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Ref: linear displacement transmitter

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