10° rotation of a motor in 0,003125 sec
This is a pure physics/mechanics question, no electronics needed. But EEs are versatile, so it can be answered here.

'Stops immediately'? Immediately is zero time, so will require infinite power. I'm sure you realise that's not going to happen.

You need therefore to think about a finite time where the motor accelerates to speed, and a similar braking time at the end.

Let's add one 0.003125 time step (= ts = 1/320th second) to each movement, so 10 degrees takes 2*ts, 100 degrees takes 11*ts. A one step movement therefore accelerates to travel speed during the first ts, moving 5 degrees, and brakes to zero during the second ts, travelling a further 5 degrees. If it's shifting 100 degrees, it accelerates through 5 degrees during the first ts, travels 90 degrees in the next 9 steps, and brakes during the last one for the last 5 degrees of travel.

Travel speed w is therefore 1 circle in 36*ts = 8.88 rps = 533 rpm = 55.8 rad/s.

Acceleration a, if assumed to be linear over one ts, is w/ts = 55.8/ts = 18.8k rad/s.

Torque T over the acceleration time step is a*MOI = 18.8k * 0.001232 = 23Nm.

Motor power P at the end of the acceleration time step is T*w = 1360 Watts, or a mean power of about 700 W over that time.

I don't know what motor you were hoping to use, but (after 'Jaws') I think you're going to need a bigger motor. Or a lighter cam mechanism. Or a slower operation.