Announcements :Announcements Homework for tomorrow… (Ch. 8, Probs 3 & 18) Office hours… MTWRF 11-noon


Chapter 8 :Chapter 8 Rotational Equilibrium & Rotational Dynamics


Section 8.1: Torque :Section 8.1: Torque Newton’s 2nd Law… Rotational Analog of Newton’s 2nd Law… “Moment of Inertia”


Torque (“to twist”) :Torque (“to twist”)  depends on the chosen axis of rotation What are the SI units? Rotation Axis ‘Tail-to-Tail’ Not Angular Displacement


Quiz Question 1 :Quiz Question 1 You are trying to open a door that is stuck by pulling on the door knob in a direction perpendicular to the door. If you instead tie a rope to the door knob and then pull with the same force, is the torque you exert increased? Yes No


Things to know about Center of Mass… :Things to know about Center of Mass… Usually easy to find from symmetry For all practical purposes… C of M = C of G Gravity acts as if mass is concentrated at the C of M Free bodies like to rotate about the C of M


Section 8.2: Torque and the Two Conditions for Equilibrium :Section 8.2: Torque and the Two Conditions for Equilibrium In general… An object in Mechanical Equilibrium… - Net external force must be zero - Net external torque must be zero


How to solve “Objects in Equilibrium” problems… :How to solve “Objects in Equilibrium” problems… Draw the system Choose a convenient rotation axis Choose a coordinate system Draw a free-body diagram Apply Apply Solve the system of equations.


Example :Example To balance, what should m2 be? What is the normal force (of the triangle on the bar)? .5 m 2.0 m m1 =100 kg m2


Quiz Question 2 :Quiz Question 2 A 1-kg rock is suspended by a massless string from one end of a 1-m measuring stick. What is the mass of the measuring stick if it is balanced by a support at the 0.25-m mark? 0.25 kg 0.5 kg 1 kg 2 kg 4 kg Impossible to determine


Quiz Question 3 :Quiz Question 3 A 1 N meter stick is supported from a ceiling by strings attached at the 0 cm and 80 cm marks as shown. The tension in the string at the 80 cm mark is about: 1.2 N 1 N 0.8 N 0.6 N 0.4 N 80 cm


Example: Curls :Example: Curls What is the force of the bicep on the bone if the bicep is to curl at a constant ? 5 cm 35 cm 100N


Rotational Inertia(a.k.a “Moment of Inertia”) :Rotational Inertia(a.k.a “Moment of Inertia”) Rotational “heaviness” Rotational analog of mass Depends on mass and distribution of mass relative to axis of rotation


Demo :Demo Which student is stronger?


Calculating ‘I’ :Calculating ‘I’


Examples of calculating ‘I’ :Examples of calculating ‘I’ ie 1) ie 2) ie 3) Hoop R l l l


Moments of Inertia :Moments of Inertia


Quiz Question 4 :Quiz Question 4 To increase the rotational inertia of a solid disk about its axis without changing its mass: drill holes near the rim and put the material near the axis drill holes near the axis and put the material near the rim drill holes at points on a circle near the rim and put the material at points between the holes drill holes at points on a circle near the axis and put the material at points between the holes do none of the above (the rotational inertia cannot be changed without changing the mass)


Quiz Question 5 :Quiz Question 5 A constant net torque is applied to an object. Which one of the following will not be constant? angular acceleration angular velocity moment of inertia center of gravity


Quiz Question 6 :Quiz Question 6 The two rigid objects shown have the same mass, radius, and angular speed. If the same braking torque is applied to each, which takes longer to stop? A B More info is needed R R m m A B


Section 8.6:Rotational Kinetic Energy :Section 8.6:Rotational Kinetic Energy An object rotating about some axis with an angular speed  has rotational kinetic energy given by


Demo :Demo Guesstimate KEr of the bicycle wheel..


Quiz Question 7 :Quiz Question 7 Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? The hollow sphere The solid sphere They have the same kinetic energy.  


A Race! :A Race! A disk and a hoop with the same mass and radius are released together and roll down an inclined plane. The first object to reach the bottom is: The disk The hoop Neither. They reach the bottom at the same time.


Quiz Question 8 :Quiz Question 8 A force F is applied to a dumbbell for a time interval t, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater center-of-mass speed? (a) (b) no difference The answer depends on the rotational intertia of the dumbbell


Quiz Question 9 :Quiz Question 9 A force F is applied to a dumbbell for a time interval t, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater energy? (a) (b) no difference The answer depends on the rotational intertia of the dumbbell