* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Rotational Mechanics Notes
Photon polarization wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Center of mass wikipedia , lookup
Classical mechanics wikipedia , lookup
Angular momentum operator wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Angular momentum wikipedia , lookup
Coriolis force wikipedia , lookup
Accretion disk wikipedia , lookup
Length contraction wikipedia , lookup
Equations of motion wikipedia , lookup
Fictitious force wikipedia , lookup
Rotational spectroscopy wikipedia , lookup
Classical central-force problem wikipedia , lookup
Mass versus weight wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Centrifugal force wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Bell Ringer • In terms of energy, what happens to the energy of an object in free-fall? Bell Ringer • Identify one station from yesterday’s lab. –How did you change the object’s center of mass? –What did this do to the object? Center of Mass Center of Gravity (CG) • The point at the center of an object’s weight distribution – The force of gravity can be considered to act on an object at this one point • Located in the geometric center of a symmetrical object • Located in the heavier end of an asymmetrical object • May be located where there is no actual material – i.e. A donut Center of Gravity (CG) • An object which rotates/revolves about its CG moves smoothly • An object which rotates/revolves about a point other than its CG tends to wobble Center of Mass (CM) • The average position of all of the particles making up an object • Usually located very close to the center of gravity – Not the case with very tall objects – Gravity pulls harder on the bottom of the object making the bottom “heavier” Stability • An object will topple if its CG is tipped beyond its support base • An object is most stable when its CG lie below their support points – Extra work is required to lift the CG to the point of toppling Stability Stability • Three types of equilibrium: – Stable: Object balanced so that any motion will raise its CG Stability • Three types of equilibrium: – Unstable: Object balanced so that any motion will lower its CG Stability • Three types of equilibrium: – Neutral: Object balanced so that any motion will not change location of CG CG of People • Men tend to have slightly higher centers of gravity than women Bell Ringer • This is a view of the tennis ball from above. • Write down the letter of the correct path of travel as the string is cut. • DO NOT DISUSS WITH THOSE AROUND YOU Bell Ringer • Why, when carrying a large object, do you tend to learn back? Rotational Mechanics Rotational Motion • Axis: The straight line around which circular motion takes place • Rotation: When an object turns about an internal axis – The Earth rotates on its axis • Revolution: When an object turns about an external axis – The Earth revolves around the Sun Rotational Motion • Period (T): The time it takes for an object to complete one full circle – Units: seconds Two Types of Velocity – Tangential Velocity (v): The speed of an object moving along a circular path • Units: m/s • Direction of motion: –Always changing –Always tangent to the circle Two Types of Velocity v = (2pr)/T T = period of motion (s) r = radius of circular path (m) p = 3.14 Two Types of Velocity v = (2pr)/T T = period of motion (s) r = radius of circular path (m) p = 3.14 Two Types of Velocity – Rotational Velocity (w): The number of rotations or revolutions per unit time • Units: – radians per second – revolutions per minute (rpm) • i.e.) All parts of a turntable have the same rotational velocity Relating Tangential and Rotational Velocity v = rw • Therefore, for any rigidly rotating system: – All parts have the same rotational speed – Tangential speed depends on rotational speed, w, and radius, r Bell Ringer • If a car does doughnuts with a radius of 6 m and completes one full circle every 3s, what is the car’s tangential velocity? • What is the car’s rotational velocity? Which is the right path? • This is a view of the tennis ball from above. • Write down the letter of the correct path of travel as the string is cut. Why does a CD case slide across the dashboard on a turn? What really happens… What is the right answer? What is a piece of equipment that use centripetal force for a mechanical advantage? Centripetal Force • The force that causes an object to follow a curved path – “Center-seeking” force – Always directed at a right angle to the direction of motion Fc = 2 (mv )/r Centripetal Force If the centripetal force stops acting, the object will fly off in a straight line path, tangent to the circle Centripetal Acceleration • The change in velocity of an object in rotational motion, caused by the centripetal force ac = v2/r – Occurs even if tangential speed remains constant – Object is still changing direction to maintain its circular path CentriFUGal Force • “Fictional” center-fleeing force • Only felt by an object within a rotating reference frame – Simply a reaction to the centripetal force ACTION REACTION CentriFUGal Force CentriFUGal Force Action: Centripetal force pushes object into the circle Reaction: Object exerts centrifugal force back on the surface away from the circle Simulated Gravity • Comes from the centrifugal force acting on rotating object • Simulated gravity will feel stronger when: – The capsule spins faster – The object sits farther from the axis of rotation of the capsule • If sitting on the axis of rotation, the object will feel no “gravity” Bell Ringer A friend pushes you out of his car as you go around a turn. In what direction will you travel? Bell Ringer • What provides the centripetal force for a tetherball? • What is the only way to measure the centrifugal force? Bell Ringer • In order for there to be a “simulated gravity” effect, what must happen? • (in other words what must something equal to) • Examining G Forces Torque • Recall: Forces tend to make objects accelerate • Torque makes an object rotate • Torques occur when a force is applied with leverage – Note: A perpendicular push or pull gives more rotation with less effort Torque • When the applied force is perpendicular: –Force is represented by F –Lever arm (l): the distance from the axis to the point of contact Torque • Therefore, torque (t) is: t = Fl – Units: Newton meters (N.m) • The same torque can be produced with: – Large force & small lever arm – Small force & large lever arm Torque • If a force is applied directly to the CG (l = 0), no rotation will occur –Kicking a football directly in its CG (no rotation) vs. off its CG (rotation) Balanced Torques • In order for an object to remain balanced the torques on either end must balance each other • Therefore: tccw = tcw – ccw = counter-clockwise – cw = clockwise Balanced Torques Bell Ringer • What are three things that you can do to increase the amount of torque on a stubborn rusted bolt? Rotational Inertia • Recall: Newton’s Law of Inertia • There is a similar Law of Rotational Inertia: An object rotating about an axis tends to keep rotating about that axis unless acted upon by a net torque. Rotational Inertia • Rotational inertia (I) depends on the distribution of mass of an object – Objects with mass far from their CGs will have more rotational inertia Rotational Inertia Rotational Inertia • Which has less rotational inertia: – A short pendulum or a long pendulum of the same mass? • Short pendulum – A hoop or a solid disk of the same mass? • Solid disk Rotational Inertia Bell Ringer • What are three things that you can do to increase the amount of torque on a stubborn rusted bolt? Rotational Inertia Angular Momentum • Recall: Any moving object has momentum • Similarly, any rotating object has angular momentum Angular Momentum = Iw • The more angular momentum an object has, the more torque required to change it – i.e. moving bicycle vs. stationary bicycle Angular Momentum Angular Momentum Conservation of Angular Momentum • Law of Conservation of Angular Momentum: Without a balanced, external torque, the angular momentum of a system will remain constant • In an isolated system: – If I increases, w will decrease – If I decreases, w will increase Conservation of Angular Momentum Conservation of Angular Momentum