Class Notes 28 November Seriously, there was no HW? Today: Tests graded Test rework posted, due Friday Today: Rotational kinematics example Torque, Moment of Inertia Show how time differs for flag to go through photogate on rotational platter (one flag on rim, one flag on outside of the ring attachment) (note R2/R1 = about 2) Quiz class asking which will read higher speed?
Angular Kinematic Quantities Angular position q Define: 1 rev = 360º = 2prad Connection: q = l/r Angular velocity w Define: w = Dq/Dt Connection: v = wr Angular acceleration a Define: a = Dw/Dt Connection: atan = ar Use Bike wheel with tennis ball stuck in the spokes to explain these variables. Giancoli used l for arc length. Define quantities and derive connectors. NOTE difference between tangential, radial (centripetal), and angular acceleration!
Kinematic Equations
Kinematic Equations a = constant = constant
Example A 8.00-cm-diamter ball rolls without slipping. It travels a linear distance of 127 cm in 5.00 s. How many revolutions did it make, and what was its constant angular velocity? Dq = 5.05 rev w = 6.35 rad/s
Rolling and friction I claim that an object that rolls without slipping experiences no energy loss due to friction. Proof: The bottom is (momentarily) at rest and not moving *relative to the surface it is in contact with*. So distance is zero, thus so is work due to friction.
Example A wheel spinning at a rate of 120. rpms is allowed to coast to rest and does so in 30.0 s. How far does it turn? What is its angular acceleration? Here is an easier example: A disk rotates with constant angular acc. of 2.00 rad/s2. If it starts from rest find the number of revolutions and angular velocity after 10.0 s. = ?, = ? (15.9 rev, 20.0 rad/s) Dq = ?, a = ? Dq = 30.0 rev or 60p rad a = -2p/15 rad/s2
Two coins sit on a rotation platform, coin “A” at half the radius of coin “B”. Compare their line- ar and angular speeds by selecting two answers: vA > vB vA < vB vA = vB A > B A < B A = B 2015 Votes: x, x, x, x, x, 6 (So only 6 could have both correct)
Torque Torque is a measure of how much a force, acting on an object, would cause that object to rotate about a certain axis point. || = rFsinq Units: [] = N·m (but not Joules!) Direction… tP = r F Stress, about a point Must define which axis point! rFsin() is the angle between the two vectors. Vector r is from point of interest out to point where the force is applied. Explain what a “cross product” is. It is a mathematical operation…
Direction for Torque F r r F Counter-clockwise rotation Positive Negative So note that the torque vector is perpendicular to both vectors r and F.
You are using a wrench and trying to tighten a rusty nut You are using a wrench and trying to tighten a rusty nut. Which of the arrangements shown is most effective in loosening the nut? 1 2 3 4 Follow up question: List in order of decreasing efficiency. 2, 1=4, 3 2015 Votes: 1, 11, 1, 1
Homework For Wednesday: Test 5 rework on WebAssign Read Chapter 8, sections 3-4 Do Problems on Worksheet 33 Test 5 rework on WebAssign Due Friday by 5:00 PM Short answers are 1 submission Problems have 4 submissions