Whenever an object undergoes uniform circular motion, it experiences a net force directed towards the center of the circle, of magnitude
Fnet = ,
where m denotes the object's mass, v denotes its speed, and r denotes the radius of the circle it traces.
As an example, consider a biker riding her bicycle in a tight circle. She must “bank” (tilt) the bicycle at some angle q, to avoid falling off the seat. As shown in figure 1, the biker experiences two major forces: her weight, and the normal force exerted by the bicycle seat. The normal force pushes perpendicular to the surface of the seat. To excellent approximation, no other forces act on the biker.

The biker, who weighs W = 500 N, rides in a circle at speed 10 m/s, with the bicycle banked at q= 75°.

1. | The normal force on the biker is:

A. | (500 N)sin 75°

B. | (500 N)cos 75°

C. |

D. |

2. | Let N denote the answer to question 1. What net force does the biker experience?

A. | Ncos 75°

B. | Ncos 75° – W

C. | Nsin 75°

D. | Nsin 75° – W

3. | To calculate the radius of the circle traced out by the biker, what additional piece of information do you need?

A. | mk, the coefficient of kinetic friction between the bicycle tires and the ground

B. | ms, the coefficient of static friction between the bicycle tires and the ground.

C. | g, the acceleration due to gravity near the Earth's surface.

D. | none of the above; you already have enough information.

4. | If the biker didn't bank the bicycle while going in a circle, she would fall off the seat, partly because:

A. | A force would push her “outward” away from the center of the circle.

B. | A force would push her “inward” towards the center of the circle.

C. | A force would push her backwards.

D. | The net force on her would be zero.

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