Phys 201 1nd Edition Lecture 19Outline of Last Lecture I. Elastic collisionsOutline of Current Lecture II. Rotating ObjectsIII. TorqueA. Right Handed RuleIV. Moment of InertiaA. Rotational EquilibriumCurrent LectureRotating objects:A rotating object differs slightly from uniform circular motion. Uniform circular motion deals with a small object attached to something else rotating around an axis. Rotating objects refers to a large object, such as a door on a hinge or a plank on a nail, rotating around an axis. In this case, θ is a better way to describe the motion of the object. We describe a rotating object in terms of angular acceleration (α), which is just the change in (ω) angular velocity (Δθ/Δt) over the change in time. Describing the motion ofa rotating object is very similar to describing linear motion of an object. LinearMotionRotatingMotion x θ V ω a α t t Torque:Torque can be thought of as a measure of how much the force acting on an object can cause that object to change. The simplest equation for torque(T) is T=rF, where r is the distance from pivot point that the force (F) is acting on the object. For torque to work, r and F must be perpendicular to one another. This perpendicular position of these two vectors is called the lever arm. We get the same measure for torque no matter what angle the object is directed in as long as the force is horizontal. These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. x=x0+Vit + .5at2  θ=θ0+ω0t+.5αt2V=V0+at  ω=ω0+αtV2=V02+2a(x-x0)  ω2=ω02+2α(θ-θ0)A less simplified version of the torque equation is T=rFsin(θ). The angle is necessary to calculate the perpendicular distance of the lever arm. Magnitude of the torque is the same if you apply the force up ordown. If you consider a rotating object, remember that a change in rotational motion is angular acceleration.Right-handed rule:We need to be able to define where our axis of rotation is. Once we’ve defined axis of rotation, then we can decide which way the force is applied. On way we can determine the direction of the torque of the rotation of an object is using something called the right-hand-rule. To use this rule, we put our fingers in the direction of r, and curl them to the direction of F, then the thumb points in the direction of the torque. Because rotations are 3 dimensional, this method is better than using the terms “clockwise” and “counterclockwise”.Moment of Inertia:The moment of inertia(Tnet=Iα) determines the amount of torque required to rotate an object about an axis with a certain angular acceleration. The moment of inertia depends on the amount of mass of an object and the distribution of the mass. Rotational Equilibrium:Just like in traditional equilibrium in which all forces balance, rotational equilibrium occurs when all torques balance. In other words, the sum of all torques in a system add up to zero, or no net torque. Example: An 80kg child and a 30 kg child are sitting on a seesaw. The 30kg child is 3m from the center of the seesaw. How far must the 80kg child be from the center for the seesaw to balance.For this problem, we need to find the individual torque applied by each child. In this case, force refers to the weight of the children. To find where the seesaw balances, the torques of the two children need to add up to zero.T1 + T2=0T1=-T2T1=r1*m1g  2*30*9.81=600 T2=r2*m2g  600=r2*80*9.81  r=600/800= 3/4m (from the