Problem 4: A 20-N horizontal force is applied perpendicular to the handle of the socket wrench. Determine the magnitude and the coordinate direction angles of the moment created by this force about point O. What is the moment about the z-axis?
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- Needs Complete typed solution with 100 % accuracy.3. Consider a thin rod (of width zero and uniformly distributed mass) pivoted freely at one end about the horizontal z-axis. The rod is free to swing in the xy plane (x horizontal, y vertically down). Its mass is m, and total length is l. Answer the following questions: (a) Find the moment of inertia I, for the rotation of the bar about its pivot. Use an integral along the length and write your answer in terms of m and l. (b) Write down the total angular momentum L, and the torque t, in cylindrical coordinates. Write down the equation of motion L, = t, explicitly. (c) Assuming the motion is confined to small angles, find the simplified equation of motion. Show the period of this compound pendulum. (“Compound pendulum" is used to mean any pendulum whose mass is distributed – as contrasted with a "simple pendulum," whose mass is concentrated at a single point on a massless arm.) (d) What is the length of the equivalent simple pendulum, that is, the pendulum with the same period?B/43 A badminton racket is constructed of uniform slen- der rods bent into the shape shown. Neglect the strings and the built-up wooden grip and estimate the mass moment of inertia about the y-axis through O, which is the location of the player's hand. The mass per unit length of the rod material is p. y L- L8 0
- Determine the moment of the force about point O for the following.N) Compute the moment of inertia of a solid ball of radius a about an axis if it is made of a material of constant density D (Hint: Set up the integral for I,+I, +I,, convert to spherical coordinates, integrate then divide the result by three.) Would this be much harder if the density depended on radius? How would the calculation change? The following integral is expressed in herical coorainates sp ates.The 29-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moment of P about point B and about point A. Moments are positive if counterclockwise, negative if clockwise. Ariswers: M₂- i MA-1 P = 29 N 1.2 m B 47° 1.2 m N-m N-m
- A 1 kg frog is sitting on a seesaw. Use 1ONg a) What is the torce on the seesaw, 2 m right of the pivot, due to the frog's mass? 2 m b) What is the moment about the pivot due to this mass? Is this clockwise or anticlockwise? C) A cat has a mass of 2 kg. What happens if he sits on the other side of the seesaw, 2 m from the pivot? Where does the cat need to sit so that the seesaw is balanced?A 200kg disk with a radius of 4.0m is rotating clockwise about the +y axis. A 50kg person is sitting 2.5m from the rotational axis. a) What is the total moment of inertia of the disk and person together? b) What is the initial angular momentum Li of the system? c) A constant 30.0N force is applied to the edge of the disk with an angle of 60° with respect to the moment arm. (+y out of page in top down view) What is the torque on the system? d) What is the final angular momentum if the torque is applied for 2s?The rotational form of Newton's 2nd law can be written in terms of the angular momentum as: TP = Tnet dt Select ALL statements below which are true regarding the rotational 2nd law. -avg The change in system angular momentum in a interval of time At is AL=Tnet At where Tnet is the average net torque. O The angular momentum of the system is conserved if there is no net external torque. O By Newton's 3rd law all internal torques cancel so only external torques contribute to the net torque. O The rotational kinetic energy is conserved if there is no net external torque.
- Suppose you start an antique car by exerting a force of 350 N on its crank for 0.16 s.Randomized Variablesf = 350 Nt = 0.16 sd = 0.22 m What angular momentum is given to the engine if the handle of the crank is 0.22 m from the pivot and the force is exerted to create maximum torque the entire time?1. Given the vectors M = -10āx + 4ã, – 8ả, and Ñ = 8å, + 7ã, – 2ã,, find: a. A unit vector in the direction of -M + 2Ñ b. The magnitude of 5å, + N – 3M c. M||2Ñ|(M + N)Two discs rotate freely about their vertical axis passing through their centers in the horizontal plane. The corresponding moments of inertia are I1 and I2 with angular velocities w1 and w2. The upper disc falls on the lower one, and after short time they both spin at the same steady – state angular velocity (due to friction). Find: a. The steady – state angular velocity of both discs. b. . The work done by the frictional forces during the process.