frequency power velocity

Question

2.2 A point on a wheel with a diameter of 1,6 m has a velocity of 130 m/s. Calculate the following: 2.2.1 The rotational frequency in revolution per minute 2.2.2 The angular velocity in rad/s at which the wheel is turning 2.2.3 The power required to drive the wheel if the force applied to the rim is 142 N

Answer 1

2.2.1)

Given data

Diameter d = 1.6 m

Velocity v = 130 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

= 130 / 1.6π

= 25.86

= 26 rpm

rpm = The revolutions per minute

The rotational frequency of the wheel in revolutions per minute is 26 rpm.

 

Answer 2

2.2.2)

Given data

Diameter d = 1.6 m

Velocity v = 130 m/s

The angular velocity of wheel = ?

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

= 130 / 1.6π

= 25.86

= 26 rpm

rpm = The revolutions per minute

Angular velocity  ω= rpm x (2π)/60

ω = 25.86 x (2π)/60

ω = 2.71 rad/s

Solution :

The angular velocity of wheel is  2.71 radians per second

Answer 3

2.2.3)

Given data

Diameter d = 1.6 m

Radius r = d/2

r = 1.6/2 = 0.8 m

Velocity v = 130 m/s

Force applied F = 142 N

The power required to drive the wheel P = ?

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

= 130 / 1.6π

= 25.86

= 26 rpm

rpm = The revolutions per minute

Angular velocity  ω= rpm x (2π)/60

ω = 25.86 x (2π)/60

ω = 2.71 rad/s

The torque required [Nm] at the wheels is Maximum force[N] x radius of the wheel{m]
T = F x r

T = 142 x 0.8

T = 113.6 N - m.

The power of a rotating wheel = Torque or moment ×  Angular velocity

P = T ω

P = 113.6 × 2.71

P = 307.86 W

Solution :

The power required to drive the wheel is 307.86 W