velocity

Question

2.1. a pulley is coupled to an input shaft rotating at 340 r/min. the diameter of the pulley is 640mm. Calculate the following: 2.2.1. the angular displacement in radians, of the pulley after 17 seconds 2.2.2. the angular velocity in rad/s at the pulley after 17 seconds 2.2.3. the linear velocity of the pullet in m/s after 17 seconds.

Answer 1

2.2.1)

Rotating rate of a shaft is 340 r/min .

The diameter of the pulley is 640mm .

The angular displacement is (Angular speed of shaft (RPMs)) * (2π) .

                                      = 340 RPM * 2π 

                                      = (340/60 revolutions/second ) *  2π  

                                     = 5.666 *  2π 

                                    = 35.6047 

Angular displacement after 17 sec is = 35.6047 *17 

                                                       = 605.280 revolutions .

So the angular displacement after 17 sec is ≈ 605 revolutions .                                                            

Answer 2

2.2.2)

The angular displacement is (θ ) = 605.280 radians 

 The angular velocity can be found by the formula w = θ / t

Where θ is angular displacement 

         t is time = 17 sec 

w = θ / t   ⇒ 605.280 / 17 

w = 35.604 radians / sec . 

So the angular velocity is 35.604 radians / sec .

Answer 3

The diameter of the pulley is 640mm  = 0.64 m.

The radius of the pulley is r = 0.64/2 = 0.32 m

The angular velocity is 35.604 radians / sec . 

The Linear velocity and the angular velocity of any body moving in curved path is given by: 

                                                                     V = w r

Where V linear velocity 

             w is angular velocity 

             r is moving path ( radius of pulley )

So linear velocity is =  35.604 * 0.32 

                           = 11.393 m/s

The linear velocity is 11.393 m/s .

 

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