Question

the constant angular acceleration of an pulley is 4 radians/sec^2 and its angular speed is 3 rad/sec. determinethe radians of the pulley if the total acceleration of a point on the rim of the pulley is 3.5m/sec^2

Answer 1

Linear acceleration = R * angular acceleration = 4R
Centripetal acceleration = R * angular velocity^2 = 9R
Net acceleration = 3.5 =sqrt( (4R)^2+(9R)^2) = sqrt ( 97R^2)
R*sqrt(97) = 3.5 , R= 0.355 m.

The radius of the pulley is 0.355 m.