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A wheel of radius 14 inches is rotating 0.5 rad/s. what is the linear speed v, the angular speed in rpm, and the angular speed in deg/s?

Respuesta :

barnuts

First, let us find for the linear speed v. The formula for this is:

v = r w

where r is radius and w is radial velocity, therefore the linear speed is:

v = 14 inches (0.5 rad / s)

v = 7 inches / s

 

Now calculating for angular speed in rpm or revolutions per minute:

angular speed in rpm = (0.5 rad / s) (1 rev / 2π rad) (60 s / min)

 angular speed in rpm = (15/π) rpm = 4.77 rpm

 

Finally calculating for angular speed in deg per second:

angular speed in rpm = (0.5 rad / s) (360° / 2π rad)

 angular speed in rpm = (90/π) deg/s = 28.65 deg/s

Lanuel
  1. The linear speed (V) is equal to 7 in/s.
  2. The angular speed in rpm is equal to 4.77 rpm.
  3. The angular speed in deg/s is equal to 28.65 deg/s.

Given the following data:

  • Radius of wheel = 14 inches.
  • Angular speed = 0.5 rad/s.

To determine linear speed (V):

How to calculate the linear speed.

Mathematically, linear speed is given by this formula:

[tex]V=rw[/tex]

Where:

  • w is the angular speed.
  • r is the radius.

Substituting the parameters into the formula, we have;

V = 14 x 0.5

Linear speed, V = 7 in/s.

For the angular speed in rpm:

Note: Rpm simply means revolutions per minute.

Angular speed (rpm) = \frac{0.5 \times 60}{2 \pi}

Angular speed (rpm) = \frac{30}{2 \times 3.142}

Angular speed (rpm) = \frac{30}{6.284}

Angular speed (rpm) = 4.77 rpm.

For the angular speed in deg/s:

Angular speed = \frac{0.5 \times 360}{2 \pi}

Angular speed = \frac{180}{6.284}

Angular speed = 28.65 deg/s.

Read more on angular speed here: https://brainly.com/question/4183355

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