Circular Motion: Forces

Centripetal Force All objects that experience circular motion experience a centripetal force. The centripetal force is the “center seeking” force. It points to the center of the circle of the motion.

Centripetal Force, pt 2 No matter where the object is in the circle, the centripetal force points toward the center.

Centrifugal Force From the object’s frame of reference there is an outward force. This is the centrifugal force.

Bucket of Water Swung In A Circle Is there a force pointing outwards that is keeping the water in the bucket? If a bucket of water is swung in a circle the water will stay in the bucket even when it is upside down. There is an apparent force that pushes the water to the bottom of the bucket which is called the centrifugal force. It is often called a “fictitious” force because there is no actual force pushing on the water. The centrifugal effect is caused by inertia and centripetal acceleration.

Inertia Force? No, it’s Inertia

Centripetal Force

Uniform Circular Motion A 2.0 kg ball completes 3 revs in 6 seconds. What is Fc? r = 0.5 m

Finding v

Fc

Centripetal Acceleration

Non-Uniform Circular Motion A ball attached to a string moves in a vertical circle. If v = 5 m/s at the point indicated, what is the total acceleration? r = 0.5 m

Total Acceleration The total acceleration is the combination of the centripetal acceleration and the tangential acceleration. aC aT

Non-Uniform Acceleration, Pt 2 FT Fg FT FT FT Fg Fg Fg

r = 0.4 m m = 1 kg What is the min. speed to remain in circular motion? FT Fg The minimum speed occurs when FT=0

Tmax=300 N m = 10 kg r = 0.4m What is v max. without breaking the rope? FT Fg

Roller Coaster A roller coaster has a circular loop that has a 10.0 m radius. It is desired that the occupants feel an acceleration of 1 g pushing them into the seat at the top of the loop. What is the necessary speed at the bottom of the loop that will allow for this condition at the top? (Assume the roller coaster is frictionless)

Model FN Fg K+U at top Just K at bottom Frictionless=Mechanical Energy Conserved Person “feels” FN as a force pushing up into seat K+U at top FN Fg Just K at bottom

To feel a sensation of 1g acceleration into the seat, FN = Fg

Conservation of Mechanical Energy