Final answer:
Even with a frictional force balancing the gravitational component and preventing translational motion, an applied torque could still cause a ball on a ramp to spin in place if it is large enough to overcome any static frictional resistance to rotation.
Step-by-step explanation:
If we have a ball on a ramp with angle θ which results in a gravitational component acting along the ramp equal to mgsin(θ), and a friction force that is exactly equivalent to this force, the ball should remain static according to Newton's second law; there should be no net translational motion as the forces are balanced.
However, if there's a torque applied, the situation for rotational motion differs. We must consider that torque is the rotational analog of force, implying that a torque could cause the ball to spin even without it rolling down the ramp, provided there is no rotational static friction opposing the torque.
The angular acceleration is given by α = τ/I, where τ is the torque and I is the moment of inertia. If the torque is sufficient to overcome static frictional forces, the ball will spin in place.