First do the maths....

You want to accelerate and then decelerate going 2pi/25 radians in 1/25th of a second

Just the acceleration takes you pi/25 radians in 20ms, and w = 0.5 a.t^2, gives a = 628 rad/s/s.

Lets say your turntable weighs 1kg, with even density, radius 25cm. Then its MoI is 0.25 M R^2,

or 0.0156 kg m^2.

torque = MoI x angular acceleration, ie 628 * 0.0156 = 9.8 Nm

Peak angular velocity is 0.02 x 628 = 12.5 rad/s (120 rpm).

torque x speed = 122W peak mechanical power required.

So you need a servo motor of 150W or more. Yes it will vibrate like crazy, because you

are vibrating it like crazy...

So what are you actually trying to do?