revolutions velocity rational-frequency

Question

2.2 A point on the rim of a wheel with a diameter of 1,76 m has a velocity of 396 km/h. Calculate the following: 2.2.1 The rotational frequency of the wheel in revolutions per minute 2.2.2 The angular velocity of the wheel in rad/s 2.2.3 The number of revolutions made by the wheel during 36 minutes

Answer 1

2.2.1)

Given data

Diameter d = 1.76 m

Velocity v = 390 km/h

1km/h = (5/18) m/s

v = 390 (5/18) m/s

v = 108.33 m/s

The rotational frequency of the wheel in revolutions per minute (rev/min) = ?

The number of circumferences of wheel which fit inside the total distance is the number of times the wheel revolves( rev/min) in that time period.

The number of revolutions per minute = (speed) / (circumference of wheel)

The number of revolutions per minute  (rpm ) = v / πd

= 108.33 / 1.76π

= 19.602

= 20 rpm

rpm = The revolutions per minute

The rotational frequency of the wheel in revolutions per minute is 20 rpm.

 

Answer 2

2.2.2)

Given data :

Diameter d = 1.76 m

Velocity v = 390 km/h

1km/h = (5/18) m/s

v = 390 (5/18) m/s

v = 108.33 m/s

he rotational frequency of the wheel in revolutions per minute (rev/min) = ?

The number of circumferences of wheel which fit inside the total distance is the number of times the wheel revolves( rev/min) in that time period.

The number of revolutions per minute = (speed) / (circumference of wheel)

The number of revolutions per minute  (rpm ) = v / πd

= 108.33 / 1.76π

= 19.602

= 20 rpm

rpm = The revolutions per minute

Angular velocity  ω= rpm x (2π)/60

ω = 19.602 x (2π)/60

ω = 2.05 rad/s

Solution :

The angular velocity of wheel is  2.05 radians per second

Answer 3

2.2.3)

Given data

Diameter d = 1.76 m

Velocity v = 390 km/h

1km/h = (5/18) m/s

v = 390 (5/18) m/s

v = 108.33 m/s

The number of revolutions made by the wheel during 36 minutes = ?

The number of circumferences of wheel which fit inside the total distance is the number of times the wheel revolves( rev/min) in that time period.

The number of revolutions per minute = (speed) / (circumference of wheel)

The number of revolutions per minute  (rpm ) = v / πd

= 108.33 / 1.76π

= 19.602

= 20 rpm

It means for 1 minute wheel rotates 20 revolutions

For 36 minute wheel rotates 20×36 revolutions.

20×36 = 720 revolutions.

The number of revolutions made by the wheel during 36 minutes is " 720 "