Question

A flywheel with the radius of 0.360 m starts from rest and accelerates with a constant angular acceleration of 0.520rad/s^2.Compare the magnitude of the tangential acceleration, the radial acceleration ant the resultant acceleration a)rim at rest b)turned through 60 degree c)turned through 120 degree.

Answer 1

here,

angular accelration , aa = 0.52 rad/s

radius , r = 0.36 m

a)

when flywheel at rest ,

radial accelration is zero as the flywheel at rest

tangential accelration , at = r*aa

at = 0.19 m/s^2

the resultant accelration is 0.19 m/s^2

b)

let the angular velocity at 60 degree( theta = 1.05 rad) be w

using third equation of motion

w = sqrt( 2*theta*aa)

w = 1.04 rad/s

the radial accelration , ar = r*w^2

ar = 0.39 m/s^2

tangential accelration , at = r*aa

at = 0.19 m/s^2

the resultant accelration , a = sqrt( 0.19^2 + 0.39^2)

a = 0.43 m/s^2

the resultant accelration is 0.43 m/s^2

c)

let the angular velocity at 60 degree( theta = 2.1 rad) be w

using third equation of motion

w = sqrt( 2*theta*aa)

w = 1.48 rad/s

the radial accelration , ar = r*w^2

ar = 0.79 m/s^2

tangential accelration , at = r*aa

at = 0.19 m/s^2

the resultant accelration , a = sqrt( 0.19^2 + 0.79^2)

a = 0.81 m/s^2

the resultant accelration is 0.81 m/s^2