Apulley with a radius of 10.0 cm is mounted on an axle that passes through the center of the pulley. the axle allows the pulley to rotate with negligible friction. the pulley is initially at rest. at t = 0, you start pulling on the end of a string that is wrapped around the outside of the pulley, giving the pulley a constant angular acceleration of 2.90 rad/s2. after t = 3.00 s of you pulling on the string, calculate the instantaneous speed of a point on the edge of the pulley (m/s)

Answer

given,                                  

radius of the pulley  = 10 cm

                                 = 0.1 m

angular acceleration = 2.9 rad/s²

time = t = 3 s

ω = ?                                    

ω = α t                                                              

ω = 2.9 x 3                  

ω = 8.7 rad/s      

angular speed of the pulley = 8.7 rad/s                  

speed at a point

v = r ω                            

v = 0.1 x 8.7                              

v = 0.87 m/s      

speed at any point in the pulley = 0.87 m/s                          

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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