A solid, uniform disk of radius 0.250 m and mass 55.0 kg rolls down a ramp of length 4.50 m that makes an angle of 15.0∘ with the horizontal. The disk starts from rest from the top of the ramp. Find the speed of the disk’s center of mass when it reaches the bottom of the ramp. I see alot of answers that set up an energy equation like so:
mgh = 1/2 mv^2 + 1/2 Iw^2

But they they say w = v/r and replace it with v/r, solving for v. However, the v from this equation should be tangential speed, but the equation is asking for the speed of the center of mass. Are they the same speed?