AIRPLANE WHEEL 60 POINTS A APM 1000 A RPM after B seconds m

AIRPLANE WHEEL.. (60 POINTS)... A (APM) 1000 = (A) RPM after (B) seconds mass = (C ) kg diameter (D) meters 2sec. meters ( 200 D = o.. FIND: a(1/s^2): Oat (3) seconds: (revolutions) at (3) seconds: (radians) Horizontal velocity at (3) seconds with wheel on runway (meters/second): Total kinetic energy of wheelTorque applied to wheet at (3) seconds (angular and linear) (joules): (NM): Power delivered to wheel only for angular acceleration (watts):

Solution

angular velocity = 1000 rpm or 104.72 rad/s

angular acceleration = angular velocity / time = 104.72 / 2 = 52.36 rad/s^2

angular displacement (theta)   = 0.5 * angular acceleration * t^2

at t = 3s

angular displacement (theta)   = 0.5 * 52.36 * 9   = 235.62 radians

angular displacement (theta) in revolutions = 235.62 / 2 * pi   = 37.5 revolutions

horizontal velocity   = angular velocity * radius of wheel

                            = 52.36 * 3 * 0.75/2    = 58.905 m/s

total kinetic energy   = 0.5 m v^2 + 0.5 * I * w^2    ( I = m*R^2/2)

                               = 0.5 * 1.5 * 200 * 58.905^2    = 520.47 kJ

Torque applied to wheel = I * angular acceleration

                                   = 200 * (0.75/2)^2 /2 * 52.36    = 736.3125 Nm

Power = Torque * angular velocity ( t= 3 sec)

           = 736.3125 * 52.36 * 3   = 115.659 kW