Question

A flywheel with a radius of 0.200 m starts from rest and accelerates with a constant angular acceleration of 0.400 rad/s2 .

Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 ?.

Compute the magnitude of the tangential acceleration of a point on its rim after it has turned through 120.0 ?.

Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 ?.

Answer 1

here,

radius , r = 0.2 m

constant angular accelration , alpha = 0.4 rad/s^2

for theta = 60 degree = 1.05 rad

let the angular speed be w

w = sqrt(2 * alpha * theta) = 0.92 rad/s

the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 degree , ac = w^2 * r = 0.17 m/s^2

for theta = 120 degree = 2.1 rad

the tangential accelration , at = r * alpha = 0.08 m/s^2

let the angular speed be w'

w' = sqrt(2 * alpha * theta) = 1.3 rad/s

the magnitude of the radial acceleration of a point on its rim after it has turned through 60.0 degree , ac = w^2 * r = 0.34 m/s^2