Start from Newton’s 2nd Law
Direction: toward the center of the circle of motion
Centripetal force is not a new kind of force
Centripetal force refers to any force that keeps an object following a circular path
Centripetal force is a combination of
Gravitational force mg: downward to the ground
Normal force N: perpendicular to the surface
Tension force T: along the cord and away from object
Static friction force: fsmax = µsN
What provides Centripetal Force ?
Draw a free body diagram, showing and labeling all the forces acting on the object(s)
Choose a coordinate system that has one axis perpendicular to the circular path and the other axis tangent to the circular path
Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration, FC)
Use Newton’s second law
The directions will be radial, normal, and tangential
The acceleration in the radial direction will be the centripetal acceleration
Solve for the unknown(s)
A small ball of mass m = 5 kg is suspended from a string of length L = 5 m. The ball revolves with constant speed v in a horizontal circle of radius r = 2 m. Find an expression for v and a.
The Conical Pendulum
Find v and a
A 1500 kg car moving on a flat, horizontal road negotiates a curve as shown. If the radius of the curve is 35.0 m and the coefficient of static friction between the tires and dry pavement is 0.523, find the maximum speed the car can have and still make the turn successfully.
The force of static friction directed toward the center of the curve keeps the car moving in a circular path.
A car moving at the designated speed can negotiate the curve. Such a ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 13.4 m/s and the radius of the curve is 35.0 m. At what angle should the curve be banked?