Tangential velocity - This video demonstrates that once objects lose their centripetal force and leave the circle, they will travel away from the circle in a direction that is tangent to the circle at the point at which the centripetal force was lost. In this case, the objects are water droplets flying off of a bicycle wheel.
Pendulum release from horizontal position - This instructional video goes through using Newton's second law for circular motion to calculate the tension in the pendulum string at the bottom of the swing. Then we use lab equipment to perform the experiment and compare our measurements to our calculations. Finally, we see some humorous applications of the concept in the real world in the form of rope swing wipeouts.
Decreasing Vt, constant Fc - A constant force pulls on the string producing a constant centripetal force. Slight friction between the table's surface and the dry-ice puck causes a gradual decrease in the tangential velocity. Observe the effect on the radius of the circle as Vt decreases. (The constant Fc is provided by a mass under the table hanging on the string that passes thru a small hole in the table top).