1. AP PHYSICS MONDAY 15.03.09 STANDARDS: Agenda: 1.Warm Up 2.Review HW Tap#9Stamp HW 3.Review PreLab for Lab#11 4.Lab #11 Angular Motion Experience Lab 5.Tap#11 Calculations & conversions using angular motion quantities Homework Tap#10 Warm Up Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT gain experiential understanding of the concept of angular velocity by completing the 5 lab tasks as a precursor to understanding angular momentum. P-Problem Solvers Week 27 Find the rpm of a tire that rotates with a period of 0.04s.

2. AP PHYSICS TUESDAY 15.03.10 STANDARDS: Agenda: 1.Warm Up 2.Review Lab 11 & HW 11 3.Collect HW up to Tap#9 tomorrow 4.Mini Lecture: rotational vs Linear 5.Tumblebuggy Revisited #12 Homework Tap#11 Converting Problems Warm Up Compare and contrast linear velocity and angular velocity. Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT explain the similarities and differences between rotational motion and linear motion D-Disciplined Learners

3. AP PHYSICS WEDNESDAY 15.03.04 Agenda: 1.Warm Up 2.#13 Golf ball vs Marble Homework Tap#12 Warm Up A car with 60.0 cm rims is moving ahead at a speed of 12.0 m/s. Find the angular speed, period, and frequency of the tires. Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT use the rotational equations of motion to find the angular acceleration of a marble rolling down the ramp. E-Effective Communicators

4. AP PHYSICS THURSDAY 15.03.12 STANDARDS: Agenda: 1.Warm Up 2.Rotational Acceleration of a marble Lab Homework Tap #13 Rotational Motion Quiz Tomorrow (not ap questions) Warm Up A 0.002 m radius marble accelerates at 2m/s 2 down a ramp for 1.4 seconds. If it starts at rest, what is its final angular velocity? Standards: 4D net torque changes angular momentum of system I –Independent Resilient Individuals RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT use the rotational equations of motion to find the angular acceleration of a marble rolling down the ramp. P-Problem Solvers

5. AP PHYSICS FRIDAY 15.03.06 STANDARDS: Agenda: 1.Warm Up 2.Finish Acceleration Lab 3.Take Angular Motion Quiz Homework Tap#13 Warm Up Free Day Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT understand the factors affecting the motion of objects moving translationally and rotationally. P-Problem Solvers

6. TAP#2 1.(1) The nests built by the mallee fowl of Australia can have masses as large as 3.00x10 5 kg. Suppose a nest with this mass is being lifted by a crane. The boom of the crane makes an angle of 45.0° with the ground. If the axis of rotation is the lower end of the boom at point A, the torque produced by the nest has a magnitude of 3.20x10 7 Nm. Treat the boom’s mass as negligible, and calculate the length of the boom. 2.(3) A meterstick of negligible mass is fixed horizontally at its 100.0 cm mark. Imagine this meterstick used as a display for some fruits and vegetables with record-breaking masses. A lemon with a mass of 3.9 kg hangs from the 70.0 cm mark, and a cucumber with a mass of 9.1 kg hangs from the x cm mark. What is the value of x if the net torque acting on the meterstick is 56.0 Nm in the counterclockwise direction? A.F=100 N r=50m τ=? B. F=20 N r=20m θ=30° τ=? C. F=10N r=4N θ=40° r F θ D. F=10N r=4N Φ=40° r F Φ

7. LINEAR VS ROTATIONAL EQUATIONS OF MOTION Position RotationalLinear x *Note: The x in rotational motion means position on the circle. More generally the equation is written s=rθ and in fact all of the linear and rotational motion equations would use an s for displacement in its most general form. Displacement Velocity, Acceleration Equation of Motion #1 Equation of Motion #2 Equation of Motion #3, * Concept Extra Credit: Use the equations for rotational position,velocity & acceleration to convert the Linear Equations of Motion into the Rotational Motion Equations. θ,

8. TAP#3 TORQUE& EQUILIBRIUM A. F=6N r=8N θ=20° F θ r m rod g F ap B. F ap =20N l=10m r=3m τ net =? m rod =5kg m block =2kg l r 1.A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance a stick? -- 36 cm 2.A meterstick of negligible mass has a screw drilled in it at the 0.60 m mark so it is free to spin. If the meterstick is stuck into the wall and a 2.0 kg mass hung at the 0m mark while you are holding up the other side, what is the magnitude of the net torque on the meterstick about the fulcrum immediately after you release the meterstick? r

9. TAP #4 TORQUE WORKSHEET PROVIDED TO YOU TAP#5 CENTER OF MASS

10. #9 CENTER OF MASS LAB ACTIVITY 2. Take a 20g and 40g mass. If the pivot point is at the 50 cm mark on the ruler and the 20g mass is placed at the 70 cm mark, where should you put the 40g mass to make the center of mass hit the pivot point. Calculate, then check your work by testing out your calculated position. 3. Take a 10 g mass. Place the 10g mass on the 80 cm mark. Where should you make the pivot point so that it touches the center of mass and the ruler balances? Calculate then test with a ruler and masses. 1. Find the center of mass of a 100 g mass at the 75 cm mark and a 200 g mass at the 25 cm mark. Will there be a net Torque associated with this center of mass? Calculate the net Torque at the center of mass. 4. A 100 g mass is at the 90cm mark on a ruler that pivots at the 50 cm mark. A 500 g mass is at the 30 cm mark on the same ruler. Where would a 200 g mass need to be placed to make the center of mass hit the 50 cm mark. Calculate then verify.

11. #10 TORQUE ON A HINGE JOINT Theory Torque is a force at a radius. Specifically a torque (twist) is caused when a force is applied perpendicular to a radius. The Greek letter τ, tau, is used for torque. Torques can act clockwise and counterclockwise and thus torque is a vector. The vector sum of all the torques on a system is called a net torque. The formula for any single torque is τ=r x F or |τ|=r F perpendicular where only the perpendicular component of the force causes a torque. Apparatus Details The set up illustrated above is a system of variable torque. However, since rotational will not occur, the net torque will be 0 in all cases. For simplicity, we will agree to assign the hinge (pivot) as the zero point. On the diagram at right, draw labeled vector arrows for the three forces causing torques: the weight of the mass M, the weight of the plank m, and the Tension T. There is another force on the plank; it is the normal force from the hinge. Can you convince yourself that (if you were to draw it) it would point up and to the right? Both weights’ torques point downward (clockwise), the tension’s point upward (counterclockwise). However, the tension is not straight up. Since only perpendicular force can cause a torque, draw and label sine and cosine components of the tension. Label each component. Questions i According to the figure on the left, what is the torque from the hanging mass, M ii.What is the torque from the plank’s mass? iii.What is the torque from the rope’s tension? iv.Can you prove that the normal force provides no torque? v.Which is the larger? The torque from the two masses, or the rope’s? Explain. Spring Scale Hinge T m M R L h

12. TAP#6 TORQUE ON A HINGE JOINT This is a setup that may be given on the AP Test so lets get to know it. 1.Find the Center of Mass of this 2 mass system. 2.Find the Torque caused by the the uniform density hinged rod. 3.Find the Torque caused by the hanging mass. 4.Find the Torque caused by the Rope. 5.Find the angle between the rope and the hinged rod 6.Find the component of Tension that causes Torque 7.Find the component of Tension that is wasted (that does not produce Torque) 8.Find the Tension reading on the spring scale. 9.Give yourself a pat on the back for finishing!!! Spring Scale Hinge T 500g 40cm 50cm 30cm A. 80g

13. TAP#8 & #9 & #10 & #11 SEE SHEET

14. ROTATIONAL MOTION OF TUMBLEBUGGY ACTIVITY #12 We understand the linear motion of a tumblebuggy, but lets also describe the angular component of motion on the tumblebuggy. 1)Find the speed of the tumblebuggy. 2)Find the angular speed of each of the tumblebuggy wheels. 3)Find the frequency and period of rotational of the tumblebuggy tires. 4)How many rpm’s does the tumblebuggy produce? 5)Write a paragraph explaining how you might attempt to find the torque produced by the wheels. Include the information and the devices you would need to use in order to measure it.

15. #13 ANGULAR ACCELERATION LAB You will revisit the motion of objects accelerating down a ramp. Engage: Golf Ball vs Marble Rotational Motion Racing Match -Predict: Will a golf ball or a marble contain a greater angular acceleration? Will their final linear velocities be the same or different? Test: Your Objective is to compare the angular acceleration and final velocity of a golf ball vs. the marble. Interpret: What are your results? Do they seem reasonable? Explain the physics in a paragraph.