Asolid cylinder with a radius of 5.08 cm starts from rest at the top of a 12.0 meter long ramp inclined 20.3° above the horizontal. when it reaches the bottom of the ramp 3.25 seconds later the cylinder has a final linear velocity of 7.38 m/s .what was the average angular velocity of the cylinder?

w = 145.189 rad/s

Explanation:

See it in the picture.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west