Torque and Moments of Inertia Physics 111 Torque and Moments of Inertia

Equations: Torque (t) = F * L T=F * d sin ɵ If not rotation- Delta Fy: 0 Delta Fx: 0 Torque : 0 For uniform distribution of mass Weight is @ .5 L Summation of t = I ᾰ I = Summation of mr^2

Problem 1 - The pull cord of a lawnmower engine is wound around a drum of radius 6 00 cm while the cord is pulled with a force of 75.0 N to start the engine. What magnitude torque does the cord apply to the drum?

Solution: T = r*f (.06 * 75) = 4.5 N * m

Practice Problem 2: Revolutionaries attempt to pull down a statue of the Great Revolutionaries attempt to pull down a statue of the Great Leader by pulling on a rope tied to the top of his head. The statue is 17 m tall, and they pull with a force of 4200 N at an angle of 65° to the horizontal. What is the torque they exert on the statue? If they are standing to the right of the statue, is the torque positive or negative?

Solution: Given: height= 17m F = 4200 Angle = 65 Find: torque First find the length between the axis of rotation and the line of action sin(65) = 17 m / L L = 17 m / sin 45 = 20 m T = l * F = 20 * 4200 = 83910 N. m Is positive, so moving ccw

Practice Problem: What is the rotational inertia of a solid iron disk of mass 49 0 kg with a thickness of 5 00 cm solid iron disk of mass and a radius of 20.0 cm, about an axis through its center and perpendicular to it? Need to use moments of inertia of common shapes table!

Solution: For disk I = .5 mr^2 Need to convert cm to meters. I = .5 ( 49)(.2)^2 = .98 kg * m^2

Problem: Find the moment of inertia of the system below. The masses are m1 an d m 2 and they are separated by a distance r. Assume the rod connecting the masses is massless. ( moving ccw) Take m1 = 2.00 kg, m2 = 1.00 kg, r1= 0.33 m , and r2 = 0.67 m. M2 M1

I = summation of mr^2 I = m1r1^2 + m2r2^2 Solution: I = summation of mr^2 I = m1r1^2 + m2r2^2 = (2 kg)(.33m)^2 + (1 kg)(.67m)^2 = .67 kg m^2

Part 2 : What is the moment of inertia if the axis is moved so that is passes through m1? What does this mean?

Solution Part 2: I = summation of mr^2 I = m1r1^2 + m2r2^2 = (2 kg)(0)^2 + (1 kg)(1 m)^2 = 1 kg m^2 Moment of Inertia increased!