* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Power point review
Dynamic substructuring wikipedia , lookup
Classical central-force problem wikipedia , lookup
N-body problem wikipedia , lookup
Velocity-addition formula wikipedia , lookup
Density of states wikipedia , lookup
Numerical continuation wikipedia , lookup
Old quantum theory wikipedia , lookup
Quasi-set theory wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Electromagnetic mass wikipedia , lookup
Center of mass wikipedia , lookup
Mass versus weight wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Tensor operator wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Centripetal force wikipedia , lookup
Angular momentum wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Moment of inertia wikipedia , lookup
Photon polarization wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Rigid rotor wikipedia , lookup
Magnetorotational instability wikipedia , lookup
Angular momentum operator wikipedia , lookup
Pg. 123-125; Chapter 11 Circular Motion- Object spins around an external axis Ex. KD-4 Lab, horses on a carousel, swinging bat Rotational Motion-Object spins around its own center of gravity (it’s own internal axis) Ex. bicycle wheel, earth, globe, carousel, wind mill, somersault Center of mass/gravity-The average position of weight distribution To find center of gravity: balance an object Linear Rotational/Angular Displacement (d) Angular Displacement (Θ) Units: (m, km, cm) Units: (degrees, revolutions, radians) 1 m = .001 km=100 cm 360°=1 rev=2л radians d Linear Rotational/Angular Velocity (v) Angular velocity– (ω) Unit: (m/s) Unit: (rev/s, rad/s) Formula: v =∆d/∆t Formula: ω=∆Θ/∆t -need to convert to rad/s using formulas Linear Rotational/Angular Acceleration (a) Angular Acceleration (a) Unit: (m/s²) Units: (rev/s², rad/s²) Formula: a=∆v/∆t Formula: a=∆ω/∆t Linear Rotational/Angular Inertia”Laziness” Rotational Inertia (I) –Resistance to rotation “Laziness” of a rotating thing Depends on Depends on mass AND where the mass is!!! mass (m)kg Unit: kgm² Formulas: Thin ring: I=mr² Solid sphere: I= 2/5 mr² Solid disk: I = ½ mr² What is the rotational inertia of a .50 kg basketball with a radius of .15 m? Inertia for a hollow sphere I = 2/3 m r2 I = 2/3 (.50kg) (.15m)2 I = .0075 kg m2 Depends on the mass and how the mass is distributed Mass on outside (away from center of rotation) = high rotational inertia (more “laziness”) Ex) Hollow sphere Mass close to center of rotation = low rotational inertia (less inertia) Ex) Solid disk Increase rotational inertia by increasing the distance between the bulk of the mass and axis of rotation (Ex: tight-rope walker) Decrease rotational inertia by decreasing the distance of the mass to the center axis (choke up on bat, bend legs when run) Linear Rotational/angular Force (F) Torque () Unit: Newton (N) Formula: = F x r Unit: Nm Formula: F = m a Formula: = I a F x r= I a 1. Apply force perpendicular to lever arm 2. Increase length of lever arm Linear Rotational/Angular Kinetic Energy (K.E) Kinetic Energy (K.E.) Unit: Joule (J) Unit: J Formula: K.E. = ½ m v² Formula: K.E. = ½ I ω² Work (W) Work (W) Unit: Joule (J) Unit: J Formula: W = Fd Formula: W = Torque Θ Momentum (p) Angular Momentum (L) Unit: kgm/s Unit: kgm²/s Formula: p = mv Formula: L = Iω Conservation of Angular Momentum-Angular momentum remains constant during rotation unless an outside force acts on it Rotational inertia can be changed “in midflight” by rearranging mass Precession- The motion resulting from the sum of 2 angular velocities Caused by a torque Ex. bicycle rider, a top, gyroscope