I don't mean to be gross, but this is a true story {not as bad as the picture below}. In J'th grade algebra, your future physics professor was stabbed in the hand with a pencil by his best friend Juan Gonzales [1 did not change Juan's name since he does not need protection and is not innocent]. Juan planned to pretend to stab me, but then tum his wrist at the last moment and punch me instead. Not knowing this, I reached for Juan's wrist and was stabbed in the palm as he turned his wrist. Normal tattoos consist of ink pushed under the skin with a needle. I have proof in the palm of my left hand {looking at it as I write this problem} that a graphite pencil does exactly the same thing and lasts 46 years {so far}. We will assume that the velocity of Juan's hand and the pencil were both 2.2 meters per second prior to impact and that his wrist added an angular velocity to the pencil of B radiansfsecond. In reality the pencil dug in nearest to my thumb and did not poke through the back. For the purpose of this calculation we will instead say that the violet pencil of mass M and length of L pushed through my hand until 15% of its length was behind the hand. We will further assume that the normal force between the hand and the pencil was 360 Newtons and that the area of the point of the pencil was 0.0044 mm2. The coefcient of kinetic friction between the pencil exterior and my flesh was I13]r because I was running a slight fever and had a temperature of 99 degrees Fahrenheit. Determine all the following: Write an expression for dm: dm = |:| Write the TEEN\": for the Moment of Inertia: I = |:| . The formula for Moment of Inertia in the form of an integlal: I = I |:| Write an expression for the upper limit of the integral: Upper Limit 2 |:| Write an expression for r: r = Write an expression for the lower limit of the integral: Lower Limit 2 |:| HDTE: - Don't enter limits tor the integral formula, just supply the integrand. - Be careful with signs. - Be careful with capitalization. - Use at least 3 decimal places for the number in Moment of Inertia formula