As has been said, its a matter of contact speed.
The circular pathway allows more contact time between your spinning wheel and the frisbee. This gives the wheel more time to accelerate the frisbee to more closely match its own tangential velocity.
In a linear pathway, the wheel touches the frisbee for a fraction of a second; thus, a fraction of the speed of the wheel is delivered to the frisbee.
Of course, there's dark magic with various other variables such as the compression of the frisbee, space between wheel and a guide rail, type of wheel, surface area of wheel, as well as the torque and speed of the accompanying motor.
It's a matter of testing

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