3Q LQ 1

• ∑𝑭 = 𝟎


  ∑𝑭𝒙 = 𝟎 and ∑𝑭�� = 𝟎
• Objects not in Equilibrium

  An object that is accelerating
• Free Body Diagram construction:
• Forces

  • Frictional Force (fs, fk)
  • Tension Force (T)
  • Normal Force (N)
  • Applied Force (F)
  • Gravity (w)
• Free Body Diagram


  Represent forces (direction) acting on an object with arrows
• Objects in Equilibrium

  An object not accelerating<br>All forces are balanced
• ∑𝑭 = 𝟎


  ∑𝑭𝒙 = 𝟎 and ∑𝑭𝒚 = 𝒎𝒂
• Uniform Circular Motion


  • period (T)
  • v - tangential velocity (m/s)
  • r - radius
  • T - period, time for 1 complete revolution
• Direction in Uniform Circular Motion

  • Velocity is always directed tangent to the circle
  • Acceleration is always directed towards the center
• Tangential vs Angular Quantities


  • (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m? What is this angle in degrees? (b) An arc 14.0 cm long on the circumference of a circle subtends an angle of 180 degrees. What is the radius of the circle? (c) The angle between two radii of a circle with radius 1.50 m is 0.700 rad. What length
• Uniform Circular Motion


  • A ball tied to a string
• Uniform Circular Motion


  • ac - centripetal/radial acceleration (SI unit: m/s2)
  • Fc - Centripetal force (Unit: Newton)
  • r - radius
  • m - mass
• Tangential vs Angular Quantities


  • s = rθ
  • v = rω
  • a = rα
• Uniform Circular Motion

  • Motion of an object in a circle at a constant speed of rotation
  • Acceleration is constant
  • Velocity is always changing direction
• Uniform Circular Motion


  • Velocity magnitude is constant
  • Acceleration magnitude is constant
• Example: A 185-gram smartphone connected to its charging cable is playfully whirled in a horizontal circle where it completes one revolution in 0.667 s. Its rotation is clockwise when viewed from the top. If the radius of the circular path is 78.0 cm, what are the magnitudes of the smartphone’s (a) tangential velocity and (b) centripetal force through the cable
• Moment of Inertia of Different Shapes

  • Comparison of moment of inertia for different shapes
• What is this angle in degrees?
• Dynamics of Rotation

  • Study of dynamics in rotation
• What is the centripetal force experienced by a 60kg person at earth’s equator?
• How many seconds does it take for the propeller to turn through 35 degrees?
• Compute the propeller’s angular velocity in rad/s
• What is the radial acceleration of an object at the earth’s equator? Give your answer in m/s2 and compare your answer with the value of g
• An arc 14.0 cm long on the circumference of a circle subtends an angle of 180 degrees
• Angular vs "Linear" Quantities

  • Comparison between angular and linear quantities
• The angle between two radii of a circle with radius 1.50 m is 0.700 rad
• Dynamics of Circular Motion

  • Study of dynamics in circular motion
• Moment of Inertia


  • Definition and characteristics of moment of inertia
• Force vs. Torque


  • Comparison between force and torque
• Rotational Relationships

  • Relationships between rotational quantities
• Newton’s Law of Universal Gravitation

  Any two objects attract each other with a gravitational force, proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts in the direction of the line connecting the centers of the masses
• Questions:
• The force keeping the moon in its orbit is gravitational force
• Henry Cavendish’s experiment determined the proportionality constant G in 1798
• Newton’s Law of Universal Gravitation was formulated by Isaac Newton in 1666, England (45 years after Kepler)
• Problem 3: Find the value of the gravitational acceleration g. The mass of the earth is 6.0 x 10^24kg
• Problem 1: Two spheres of mass 35kg are 60m apart. A) What force does one exert on the other? B) If the mass of one is tripled and the radius is quadrupled how does the force change?
• The force of gravity is considered universal
• If the planets are orbiting the sun, the force keeping them in orbit is gravitational force
• Change of Gravitational Force with Distance

  Law of universal gravitation is known as an inverse square law