Circular motion

Objects rotate when the axis is part of the moving object. Objects revolve when the axis is not part of the moving object. 2

Earth revolves around the Sun while it rotates around its north-south axis 3

Angular speed is the rate at which an object rotates or revolves. number of turns per unit of time (rotations/minute) 4

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.

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.

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 Mass (kg) Linear speed Centripetal (m/sec) force (N) Radius of path (m)

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

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.

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

A motorcycle drives around a bend with a 50-meter radius at 10 m/sec 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.

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.

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.

Newton’s law of universal gravitation: Gravitational force exists between all objects that have mass. The strength of the gravitational force depends on the mass of the objects and the distance between them.

The mass of the Moon is 7. 36 × 1022 kg. The radius of the moon is 1 The mass of the Moon is 7.36 × 1022 kg. The radius of the moon is 1.74 × 106 m. Use the equation of universal gravitation to calculate the weight of a 90-kg astronaut on the Moon’s surface. You are asked to find a person’s weight on the Moon. You are given the radius and the masses. Use: Fg = Gm1m2 ÷ r 2 Solve:

If an object is launched above Earth’s surface at a fast enough speed, it’s parabolic path will match the earth’s curvature. The motion of a satellite is closely related to projectile motion.

Project -Groups 3-4 Topics: -Amusement rides -5-10 min Presentation -Autorun Powerpoint -Must answer the guiding questions Topics: -Amusement rides -Planets -Satellites -Cars on circular racetracks -Artificial gravity