Presentations (Those who did not present before break) academic – Thursday 1/3 Welcome Back! Physics Fun Fact Presentations (Those who did not present before break) Review Unit 4 PowerPoint New Today: Universal Law of Gravitation, Satellites in Orbit, Friction! Formative (Finish for Homework!) Unit 4 Test 1/11 (Friday)

Conceptual – Wednesday 1/2 Welcome Back! Physics Fun Fact Scott Kelly – Launch Presentations (Those who did not present before break) Review Unit 4 PowerPoint New Today: Universal Law of Gravitation & Satellites in Orbit Begin Formative (Finish for Homework!)

Unit 4: Uniform Circular Motion

What is Circular Motion? The motion of an object traveling on a circular path What does Uniform mean? Consider Rotation & Revolution

Uniform Circular motion The motion of an object traveling at a constant (uniform) speed on a circular path. Consider a constant radius as well

Period (T) The time required to travel once around a circle, that is, to make one revolution SI Unit: seconds [s]

Linear Speed vs. Tangential Speed vs. Rotational Speed Linear Speed: How fast an object in a straight line. Think about speed/velocity up to this point in the course Tangential Speed: How fast an object moves along a circular path. Ex) Spinning something on the end of a string in a circular motion Rotational Speed: The number of rotations or revolutions per unit time. Ex) Revolutions per minute (Car engine)

Velocity – [m/s] Velocity of an object undergoing Uniform Circular Motion Thought Question: What is the direction of the Velocity vector of an object undergoing Uniform Circular Motion?

Centripetal

Centripetal acceleration Units: [m/s2] Example: When you round a corner in a car, the car and its contents accelerate inward, towards the middle of the turn.

Centripetal Force Force acting on an object undergoing circular motion, directed towards the axis of rotation. Centrifugal Force is the fictitious force acting outward, away from the axis.

Banked Curves Tan ˆ = v2/rg Banked curves are real world examples of uniform circular motion. On roads, this allows drivers to negotiate turns are high rates of speed (for example, exiting a highway) On racetracks, racers can travel at much higher rates of speed with an inclined racetrack.

Examples of Banked curves https://www.youtube.com/watch?v=XTipCQxJ6Ak https://www.youtube.com/watch?v=bw59JtWPOrU&t=0s&index=2&list=LLTvzgV7GP8jI_ZFsE7IyDoA Examples of Banked curves Bill Nye Video: https://www.youtube.com/watch?v=s1b_cUa9QmA&t=567s

Newton’s Law of universal gravitation Every particle in the universe exerts an attractive force on every other particle.

Universal Gravitational Constant G has the same value for all pairs of particles anywhere in the universe, no matter what their separation.

Satellites in circular orbits Gravitational pull of the Earth provides the centripetal force required to keep an object in orbit around the Earth. Satellites with a fixed radius will remain at a constant speed.

Orbital Speed of the Hubble Space Telescope The Hubble Telescope orbits 598km (598 x 103m) above the Earth’s surface. Determine the orbital speed of the telescope. Known Values: Radius of the Earth: 6.38 x 106m Mass of the Earth: 5.98 x 1024kg Answer: 7.56 x 103m/s

Friction & Uniform Circular Motion

Fc = μs mg = mv2/r Including Friction: Fc = μs FN = μs mg = mv2/r Friction equations Including Friction: Fc = μs FN = μs mg = mv2/r μs - Coefficient of static friction (NO UNIT!) Example: Dry Road μs = 0.90 Icy Road μs = 0.10 Fc = μs mg = mv2/r