Question

13. The constant angular acceleration of a pulley is 4 rad/s2 and its angular speed its 3 rad/s. Determine the radius of the pulley if the total acceleration of a print on the rim of the pulley is 3.5m/s2.

Answer 1

I assume that you mean a point on the rim, not a print. The radial and tangential acceleration components are perpendicular. Therefore
(3.5)^2 = (4 R)^2 + [ 3^2*R]^2
The first term on the right is the square of the tangential acceleration. The second term is the square of the centripetal acceleration.
Solve for R.

Answer 2

13. The constant angular acceleration of a pulley is 4 rad/s2 and its angular speed its 3 rad/s. Determine the radius of the pulley if the total acceleration of a print on the rim of the pulley is 3.5m/s2.