Announcements :Announcements Homework for tomorrow… (Ch. 7, Probs 30) Office hours… MTWRF 11-noon


Chapter 7 :Chapter 7 Rotational Motion and the Law of Gravity


Last time… :Last time… r  s Arc Length Rotating Body: Angular Displacement: Angular Velocity: Angular Acceleration: Rotational Kinematic Equations for Constant Angular Acceleration


Last time… :Last time… Connecting Translational & Rotational Quantities Centripetal Acceleration Newton’s 2nd Law - Centripetal Force


Quiz Question 1 :Quiz Question 1 A rider in a “Barrel of Fun” finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?


Section 7.5:Newtonian Gravitation :Section 7.5:Newtonian Gravitation The force of gravity between any two bodies is proportional to the product of their masses and inversely proportional to the square of their separation Where Direction: Attractive only


Law of Gravitation - Restrictions :Law of Gravitation - Restrictions Masses must be small compared to their separation (“point-like”) or Masses must be uniform spheres OK OK Not OK


From the MCAT… :From the MCAT… Which of the following expressions gives the acceleration due to gravity at the surface of the Earth? (Note: M is the mass of Earth, m is the mass of an observer at the surface of the Earth, and r is the radius of the Earth.) GM/r GM/r2 GmM/r GmM/r2


From the MCAT… :From the MCAT… If the gravitational force between Earth and the space station could suddenly be eliminated, which of the following diagrams would best describe the path taken by the station?


Example 1 :Example 1 What is the orbital period of the International Space Station? Kepler’s 3rd Law!!


Principle of Superposition :Principle of Superposition What is ? m1 m2 m3 m4


Principle of Superposition :Principle of Superposition This is the Principle of Superposition. m1 m2 m3 m4


Quiz Question 2 :Quiz Question 2 Four point masses, each with mass m, are arranged symmetrically about the origin on the x-axis. A fifth point mass, with mass M, is n the y-axis. The direction of the gravitational force on M is: Up Down Up and to the left Down and to the right Depends whether m>M or m

Gravitational Potential Energy, revisited… :Gravitational Potential Energy, revisited… For small displacements near the Earth’s surface… In general… The gravitational potential energy associated with an object of mass m at a distance r from the center of Earth is


Quiz Question 3 :Quiz Question 3 An object is dropped from an altitude of one Earth radius above the Earth’s surface. If M is the mass of the Earth and R is its radius, then the speed of the object just before it hits Earth is (ignoring air resistance):


Problem 1 :Problem 1 What speed is needed for an object of mass m to soar off into space and never return? This speed is commonly known as an object’s Escape Velocity


Problem 2 :Problem 2 What is the minimum initial height needed to “Loop the Loop”? h r


Problem 3 :Problem 3 A small object of mass m, on the end of a light cord is held horizontally at a distance r from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing? r