Final answer:
Tangential velocity in circular motion is always directed along the circumference of the circle and is directly proportional to both the radius and angular velocity. Uniform circular motion features constant tangential speed with changing direction, hence centripetal acceleration, while nonuniform circular motion also includes tangential acceleration.
Step-by-step explanation:
The student's question appears to concern the nature of tangential velocity in circular motion. Tangential velocity is indeed always directed tangential to the circle, or along the circumference, at any given point in the motion of an object. This is because tangential velocity is the linear velocity along the edge of the circle and is always perpendicular to the radius at any given point. The formula v = rω (where v is tangential velocity, r is the radius of the circle, and ω is the angular velocity) shows that tangential speed increases linearly with the radius for a constant angular velocity, as stated in the equation v1 = r1ω1 and v2 = r2ω2, where ω1 = ω2 due to constant angular velocity, thus v2 > v1 if r2 > r1.
If an object is undergoing uniform circular motion, it maintains a constant tangential speed, but the direction of this velocity changes continuously. The continuous change in the direction of the velocity vector is what provides the centripetal acceleration, directed towards the center of the circular path, ensuring the motion remains circular.
However, if a particle is experiencing nonuniform circular motion, it will have both centripetal acceleration (due to change in the direction of velocity) and tangential acceleration (due to change in the speed of velocity).
As for the specific case of a car spinning its tires on ice, the discrepancy between linear velocity and tangential velocity occurs because the arc length the tires travel is greater than the linear distance the car itself travels; the tangential velocity at the tires is higher due to slipping, meaning there's no actual advancement along the path despite the tire rotation.