A bicycle is turned upside down while its owner repairs a flattire. A friend spi

Question

A bicycle is turned upside down while its owner repairs a flattire. A friend spins the other wheel and observes that drops ofwater fly off tangentially. She measures the heights reached bydrops moving vertically (see figure). A drop that breaks loose fromthe tire on one turn rises vertically 54.0 cm above the tangentpoint. A drop that breaks loose on the next turn rises 51.0 cmabove the tangent point. The radius of the wheel is 0.3
(a)Neglecting air friction and using only the observed heights andthe radius of the wheel, find the wheel's angular acceleration(assuming it to be constant).74 m can't find the answer A bicycle is turned upside down while its owner repairs a flattire. A friend spins the other wheel and observes that drops ofwater fly off tangentially. She measures the heights reached bydrops moving vertically (see figure). A drop that breaks loose fromthe tire on one turn rises vertically 54.0 cm above the tangentpoint. A drop that breaks loose on the next turn rises 51.0 cmabove the tangent point. The radius of the wheel is 0.3
(a)Neglecting air friction and using only the observed heights andthe radius of the wheel, find the wheel's angular acceleration(assuming it to be constant).74 m can't find the answer

Explanation / Answer

                                Given that the initial and final heights is h1 = 54.0 cm = 0.54 m and h2 = 0.51 m                  radius of the wheel is r = 0.30 m ---------------------------------------------------------------------------------------------       due to decreasing angularvelocity first drop rise higher than the second drop             Apply conservation ofenergy for water drop                               (1/2)mU2 =mg*h1                                                                               U2 =2*g*h1                                                                                  U = (2gh1)                                                = --------- m/s           for seconddrop                                 (1/2)mv2=mg*h2                                                                               v2 =2*g*h2                                                                                   v= (2gh2)                                                = --------- m/s           Theintiial angular velocity is 1 = U / r                                                  = --------- rad/s                                             final angularvelocity after one second is   2 = v/ r                                                                               = -------- rad/s           The angular accelaration is = ( 2 - 1)/ 2                                                         =( 2 - 1) / 2*2                                                        = ( 2 - 1) / 4                                                        = ----------- rad/s2                                           radius of the wheel is r = 0.30 m ---------------------------------------------------------------------------------------------       due to decreasing angularvelocity first drop rise higher than the second drop             Apply conservation ofenergy for water drop                               (1/2)mU2 =mg*h1                                                                               U2 =2*g*h1                                                                                  U = (2gh1)                                                = --------- m/s           for seconddrop                                 (1/2)mv2=mg*h2                                                                               v2 =2*g*h2                                                                                   v= (2gh2)                                                = --------- m/s                                         v2 =2*g*h2                                                                                   v= (2gh2)                                                = --------- m/s           Theintiial angular velocity is 1 = U / r                                                  = --------- rad/s                                             final angularvelocity after one second is   2 = v/ r                                                                               = -------- rad/s           The angular accelaration is = ( 2 - 1)/ 2                                                         =( 2 - 1) / 2*2                                                        = ( 2 - 1) / 4                                                        = ----------- rad/s2                                                                                                        = -------- rad/s           The angular accelaration is = ( 2 - 1)/ 2                                                         =( 2 - 1) / 2*2                                                        = ( 2 - 1) / 4                                                        = ----------- rad/s2                         

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