Rotational Motion and the Law of Gravity Chapter 7 Rotational Motion and the Law of Gravity

Radian measure We use radian units to measure angles in angular displacement

Radian measure

Angular speed and angular acceleration Angular position Angle measured from the x axis, in radians

Angular speed and angular acceleration Angular displacement Angle measured from the x axis, in radians

Angular Velocity (ω) What is velocity? angular velocity (ω) the rate of change of angular position Units: radians per second (rad/s) Counter clockwise is positive Clockwise is negative (V) tangential speed

Angular Acceleration Rate of change of angular velocity

Angular Acceleration Rate of change of angular velocity

Circular Motion Newton’s 1st Law Newton’s 2nd Law https://www.youtube.com/watch?v=P6UwokP8BEg

Circular Motion When an object travels in a circular path, its linear velocity aka tangential velocity is constantly changing It doesn’t change in magnitude, but it is constantly changing direction. Because of this, it is often referred to as tangential speed (vt) Changing velocity is known as… In order for acceleration to take place, a _______________ is needed.

Circular Motion The net Force is directed in toward the center of the circle and is also known as a centripetal force (Fc) That force causes an acceleration that is also directed in toward the center of the circle, centripetal acceleration (ac) Fc = mac ac = (vt)2/r

The application of rotational dynamics to the space program http://science.howstuffworks.com/30275-assignment-discovery- weightlessness-in-space-video.htm

Cage of Death https://www.youtube.com/watch?v=L9aREQpcLGU Draw a free body diagram of the bike on the side of the cage, label the forces acting on the bike When the bikers are on the side of the wall, why don’t they slide down? Draw a free body diagram of the bike on the top of the cage, label the forces What holds the bikers to the top of the cage? Why don’t they fall down?

Climbing the walls… https://www.youtube.com/watch?v=5ITnzF9itKM Draw a free body diagram of the runner going up a wall, label the forces What enables the runner to go up the wall? what stops the runners’ upward progress? What rotational concepts are at play in limiting the runners’ upward progress? https://www.youtube.com/watch?v=KI4-ZHYy9IQ

Calculate Fg for an object of unknown mass at sea level (6,371 km) on the Earth (approx. 5.98x1024 kg) Calculate Fg for an object of unknown mass at the top of the tallest mountain in the world, Mt Chomolungma (8,848 m above sea level) What is the average of those two numbers?

Kepler’s Laws Kepler’s First Law All planets move in elliptical orbits, with the sun at one focus.

Kepler’s Laws Kepler’s Second Law A line that connects a planet to the sun sweeps out equal areas in equal times. When the planet is closer to the sun, it moves faster, sweeping through a longer path in a given time.

Kepler’s Laws Kepler’s Second Law Fc = Fg = G (m1m2)/r2 ac = Fc/m ac = vt2/r vt = (acr)^1/2

Kepler’s Laws Kepler's third law the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

Kepler’s Laws Kepler's third law – the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

Kepler’s Laws Kepler's third law – the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

The motion of the Sun, Earth and planets simplified… https://www.youtube.com/watch?v=vDgUmTq4a2Q https://www.youtube.com/watch?v=82p-DYgGFjI https://www.youtube.com/watch?v=BhAzMdoOe5E https://www.youtube.com/watch?v=0jHsq36_NTU