physics

• The SI unit of energy is the joule (J).
• Work done = force x distance moved in direction of force
• Power is the rate at which work is done or energy transferred.
• Kinetic energy is the energy an object has due to its motion.
• Potential energy is the energy that an object has because of its position or state.
• Conservation of energy states that energy cannot be created nor destroyed but only transformed from one form to another.
• Rotational

  Motion of a body rotated or moved from one point to another point
• Translational

  Motion of a body moved from one point to another point
• Quantities in translational motion

  • Velocity - v
  • Acceleration - a
  • Force - F
  • Mass - M
  • Momentum - p
  • Work - W
  • Power - P
  • Kinetic Energy - KE
  • Potential Energy - PE
  • Mechanical Energy - ME
• Equations of motion

  1. x = x₀ + v₀t + 1/2at²

  2. v = v₀ + at

  3. a = (v - v₀)/t

  4. F = ma

  5. W = Fd

  6. P = F·v
• Centripetal force

  Force required to make a body move along a circular path
• Non-inertial frame of reference

  A frame of reference which is accelerating with respect to an inertial frame of reference
• Relative velocity

  Velocity of one object relative to another
• Projectile motion

  Motion of an object under the influence of gravity
• Scalar

  Physical quantity with magnitude but no direction
• Vector

  Physical quantity with both magnitude and direction
• Modulus of a vector

  The length or magnitude of a vector
• Unit vector

  A vector of unit magnitude drawn in the direction of a given vector
• Equations of projectile motion

  1. x = ut cos θ

  2. y = ut sin θ - 1/2gt²
• Copyright © 2009 Pearson Education, Inc.
• Units of Chapter 10

  • Angular Quantities
  • Vector Nature of Angular Quantities
  • Constant Angular Acceleration
  • Torque
  • Rotational Dynamics; Torque and Rotational Inertia
  • Solving Problems in Rotational Dynamics
  • Determining Moments of Inertia
  • Rotational Kinetic Energy
  • Rotational Plus Translational Motion; Rolling
  • Why Does a Rolling Sphere Slow Down?

  
• Angular displacement


  The total change in angular position
• Average angular velocity


  The total angular displacement divided by time
• Instantaneous angular velocity


  The rate of change of angular position with time
• Angular acceleration


  The rate of change of angular velocity with time
• Instantaneous angular acceleration


  The rate of change of angular velocity at a specific instant
• Angular velocity (ω)


  Linear velocity (v) = ω * R

  
• Carousel or merry-go-round


  • Child on horse near outer edge
  • Child on lion halfway out from center
• Objects farther from the axis of rotation will move faster
• Tangential acceleration


  Acceleration experienced by a point on a rotating object when the angular velocity changes
• Centripetal acceleration


  Acceleration experienced by a point on a rotating object even when the angular velocity is constant
• Correspondence between linear and rotational quantities

  • Displacement (x) - Angular displacement (θ)
  • Velocity (v) - Angular velocity (ω)
  • Acceleration (a) - Angular acceleration (α)
  • Force (F) - Torque (τ)
  • Mass (m) - Rotational inertia (I)
  • Kinetic energy (KE) - Rotational kinetic energy (KErot)

  
• Carousel


  • Initial angular velocity = 0

  Angular acceleration = 0.060 rad/s2 for 8.0 s

  Determine: (a) angular velocity at t=8.0 s

  (b) linear velocity of child 2.5 m from center

  (c) tangential acceleration of child

  (d) centripetal acceleration of child

  (e) total linear acceleration of child
• Frequency


  Number of complete revolutions per second
• Period


  Time for one revolution
• Hard drive platter


  • Rotates at 7200 rpm

  Determine: (a) angular velocity (rad/s)

  (b) linear speed of reading head 3 cm from axis

  (c) bits per second written by head 3 cm from axis
• Disk rotating with ω = (1.6 + 1.2t) rad/s

  • Determine: (a) angular acceleration at t=2.0 s

  (b) speed and acceleration of point on edge at t=2.0 s

  
• Angular velocity and acceleration vectors point along axis of rotation

  
• Equations of motion for constant angular acceleration are the same as linear motion, with substitution of angular quantities

  
• Centrifuge rotor


  • Accelerated from rest to 20,000 rpm in 30 s

  Determine: (a) average angular acceleration

  (b) number of revolutions during acceleration