Objective Describe and calculate centripetal forces and accelerations. 2

Centripetal Force Why does a roller coaster stay on a track upside down on a loop? 3

Centripetal Force We usually think of acceleration as a change in speed. Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion.

Centripetal Force Any force that causes an object to move in a circle is called a centripetal force. A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.

Calculating centripetal force The magnitude of the centripetal force needed to move an object in a circle depends on the object’s mass and speed, and on the radius of the circle.

Fc = mv2 r Centripetal Force Mass (kg) Linear speed (m/sec) force (N) Fc = mv2 r Radius of path (m)

Calculating centripetal force A 50-kilogram passenger on an amusement park ride stands with his back against the wall of a cylindrical room with radius of 3 m. What is the centripetal force of the wall pressing into his back when the room spins and he is moving at 6 m/sec? You are asked to find the centripetal force. You are given the radius, mass, and linear speed. Use: Fc = mv2 ÷ r Solve: Fc = (50 kg)(6 m/s)2 ÷ (3 m) = 600 N

Centripetal Acceleration Acceleration is the rate at which an object’s velocity changes as the result of a force. Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force.

Centripetal Acceleration Speed (m/sec) Centripetal acceleration (m/sec2) ac = v2 r Radius of path (m)

Calculating centripetal acceleration A motorcycle drives around a bend with a 50-meter radius at 10 m/sec. Find the motor cycle’s centripetal acceleration and compare it with g, the acceleration of gravity. You are asked for centripetal acceleration and a comparison with g (9.8 m/s2). You are given the linear speed and radius of the motion. Use: ac = v2 ÷ r 4. Solve: ac = (10 m/s)2 ÷ (50 m) = 2 m/s2 The centripetal acceleration is about 20%, or 1/5 that of gravity.

Centrifugal Force We call an object’s tendency to resist a change in its motion its inertia. An object moving in a circle is constantly changing its direction of motion. Although the centripetal force pushes you toward the center of the circular path...it seems as if there also is a force pushing you to the outside. This “apparent” outward force is often incorrectly identified as centrifugal force.

Centrifugal Force Centrifugal force is not a true force exerted on your body. It is simply your tendency to move in a straight line due to inertia. This is easy to observe by twirling a small object at the end of a string. When the string is released, the object flies off in a straight line tangent to the circle.

v = 2π v = ω r t ω = θ θ = s t r Fc = mv² Fc = m ac r

Centripetal Acceleration ac = v² r ac = (rω)² ac = r ω²