AP Physics Monday 15.03.02 Standards: Warm Up E-Effective Commuincators m=0.4kg 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 M=2kg Learning Goal: SWBAT compare their theoretical value for Tension in a string with the one obtained through experimentation, to gain greater understanding of the physical quantity. Each dot represented 0.2 m. Find the torque contributed to the system by the tension in the string, knowing that because the bar is not moving, the system has no net torque. Agenda: Warm Up Collect HW up to TAP#5 Finish Torque on a Hinge Joint Pre-Lab/Therory Torque on a Hinge Joint Lab Homework Tap#6

AP Physics Tuesday 15.03.03 Standards: Warm Up M=1kg m=0.5kg E-Effective Communicators 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 compare their theoretical value for Tension in a string with the one obtained through experimentation, to gain greater understanding of the physical quantity Find the component of Tension that is causing a counterclockwise torque on the system, if the height from the pivot point to the spring scale is 0.5 m and each hole in the bar is 0.2 m apart. Agenda: Warm Up Collect HW up to Tap#2 Review #10 Torque Pre Lab Finish #11 Torque Lab Homework Tap#7 Torque Problems Worksheet

AP Physics Wednesday 15.03.04 Warm Up E-Effective Communicators m=1kg 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 m=1kg 20° M=2kg Learning Goal: SWBAT compare their theoretical value for Tension in a string with the one obtained through experimentation, to gain greater understanding of the physical quantity Each dot represents 0.2 m. What is the reading on the forcemeter? 3.0 m/s to the right Agenda: Warm Up Review Tap #7 Torque Lab #11 Homework Tap #8

AP Physics Thursday 15.03.05 Standards: Warm Up Each dot is 20 cm. Find M 50N P-Problem Solvers 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 m=1kg 70° M=? Learning Goal: SWBAT demonstrate how the angle of the rope affects the Torque cause by the rope. Agenda: Warm Up Review HW Tap#8 Finish #10 Torque on a Hinge Joint Lab Homework Tap #9

AP Physics Friday 15.03.06 Standards: Warm Up Review the work you’ve done so far. Find out what types of problems or what part of the concept of Torque or center of mass are you still struggling with. P-Problem Solvers 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 become familiar with the concepts associated with angular motion like angular velocity and acceleration. Agenda: Warm Up Review Tap#9 Pre-Lab Radians and angular velocity. Homework 10 question Torque quiz next Thursday

Tap#2 C. F=10N r=4N θ=40° F θ r F=100 N r=50m τ=? B. F=20 N r=20m θ=30° τ=? D. F=10N r=4N Φ=40° F Φ r (1) The nests built by the mallee fowl of Australia can have masses as large as 3.00x105kg. 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 3.20x107Nm. Treat the boom’s mass as negligible, and calculate the length of the boom. (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? 5000Nm 200Nm 25.7 Nm 30.6Nm 1.15.4 m 2. 0.50 m

Tap#3 Torque& Equilibrium F=6N r=8N θ=20° r B. Fap=20N l=10m r=3m τnet=? mrod=5kg mblock=2kg Fap l θ r F mrodg r 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 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? 45.1 Nm counterclockwise 41.2 Nm counterclockwise 1.36cm 2. 8.0 Nm

TAP #4 Torque Worksheet Provided to you TAP#5 Center of Mass

#9 Center of Mass Lab Activity 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. 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. 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.

#10 Torque on A Hinge Joint Spring Scale Hinge T m M R L h 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 Fperpendicular 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. Vector arrows, Tension up the string, M straight down, m straight down at the halfway mark of the wood. τM=MgR τt=TperpL=Tlsinθ=Th τm=mgL/2 The vertical component is at the hinge so there is no R and the horizontal component can’t cause torque. Rope balances out both masses. Questions i According to the figure on the left, what is the torque from the hanging mass, M What is the torque from the plank’s mass? What is the torque from the rope’s tension? Can you prove that the normal force provides no torque? Which is the larger? The torque from the two masses, or the rope’s? Explain.

Tap#6 Torque On A Hinge Joint Spring Scale Hinge T 500g 40cm 50cm 30cm A. 80g This is a setup that may be given on the AP Test so lets get to know it. Find the Center of Mass of this 2 mass system. Find the Torque caused by the the uniform density hinged rod. Find the Torque caused by the hanging mass. Find the Torque caused by the Rope. Find the angle between the rope and the hinged rod Find the component of Tension that causes Torque Find the component of Tension that is wasted (that does not produce Torque) Find the Tension reading on the spring scale. Give yourself a pat on the back for finishing!!! 1xcm=37.9 cm 2.τ=.196Nm τ=1.96Nm 2.156Nm 36.9° 4.3N 5.74 N 7.18 N

Tap#8 & #9 see sheet