CHAPTER 6 PLANE KINETICS OF RIGID BODIES

What are the general equations of motion for a rigid body in plane motion, as derived from the principles of force and moment for a system of mass?

What does the kinetic diagram for a rigid body in plane motion represent?

What physical property does the mass moment of inertia, I, represent for a rigid body?

What is the alternative moment equation about an arbitrary point P for a rigid body in plane motion, which expresses the principle of moments?

For a rigid body undergoing either rectilinear or curvilinear translation, what are the values of its angular velocity (omega) and angular acceleration (alpha)?

For a body undergoing fixed-axis rotation, what is the unique property of the center of percussion, point Q?

A pickup truck weighing 3220 lb has a constant acceleration of 4.84 ft/sec^2. What is the magnitude of the resultant force `ma` acting on the truck? Use g = 32.2 ft/sec^2.

A rigid bar is elevated by means of parallel links. The lower link AC has a length of 1.5 m and is subjected to a constant couple M = 5 kN-m at C. Assuming the link has negligible mass, what is the tangential component, At, of the force exerted by the hinge pin on the bar at A?

In problems involving two or more connected rigid bodies whose motions are related kinematically, when is it advantageous to analyze the bodies as an entire system?

What is the first step in the recommended Analysis Procedure for solving force-mass-acceleration problems for the plane motion of rigid bodies?

What is a primary advantage of using the work-energy method over the force-mass-acceleration method in rigid-body dynamics?

What is the correct expression for the total kinetic energy (T) of a rigid body in general plane motion, having mass m, mass-center velocity v, and angular velocity omega?

A wheel rolls on a stationary surface. Under what condition does the static friction force F acting at the point of contact do no work?

How can the kinetic energy of a rigid body in plane motion be expressed using the instantaneous center of zero velocity, C?

What is the instantaneous power developed by a couple M acting on a rigid body that has an angular velocity omega?

A 40-lb slender bar is released from rest. Its center of mass, B, is initially at the datum (Vg1 = 0). What is its gravitational potential energy, Vg2, after it moves to a position where theta = 30 degrees, causing the center of mass to drop by a vertical distance of 2(1 - cos 30) ft?

In the work-energy equation for an interconnected system, T1 + V1 + U'1-2 = T2 + V2, what does the term U'1-2 represent?

What is the primary purpose of using the work-energy equation for an infinitesimal displacement (dU = dT + dV)?

In the context of mechanics, what defines a 'virtual displacement'?

Sample Problem 6/12 uses the work-energy method for an infinitesimal displacement to find the acceleration of a rack and gear system. What is the main advantage of this method over a traditional force-mass-acceleration approach for this problem?

How is the linear momentum, G, of a rigid body defined?

For a rigid body undergoing plane motion, what is the scalar expression for its angular momentum (HG) about its mass center G?

The integrated form of the linear impulse-momentum equation for a rigid body is G1 + ∫ΣF dt = G2. What does this equation state in words?

What is the correct expression for the angular momentum HO of a rigid body in plane motion about an arbitrary point O?

Under what condition is the angular momentum of a rigid body or system of bodies conserved about a point O?

A wheel weighing 120 lb is rolling to the left with a center velocity of 3 ft/sec. Taking the direction to the right as the positive x-direction, what is its initial linear momentum, (Gx)1? Use g = 32.2 ft/sec^2.

Why is the simplified theory of impact using a coefficient of restitution (e) considered to have little practical value for the noncentral impact of rigid bodies?

What information is essential to include on an impulse-momentum diagram for a rigid body?

A 120-lb wheel with a centroidal radius of gyration of 10 inches is rolling without slipping. Its center has a velocity of 3 ft/sec. What is the magnitude of its initial angular momentum about its center, G? The outer radius is 18 inches. Use g = 32.2 ft/sec^2.

In situations involving the impact of rigid bodies over very short periods, which principles are most effective for analysis?

A 20-kg body is initially stationary. A 50-N force P is applied. The body rests on feet at A and small wheels at B, with a distance of 0.8 m between them. The coefficient of kinetic friction at A is 0.30. The center of mass G is 0.4 m above the ground and centered horizontally. If the normal force at A is found to be 81.3 N, what is the body's acceleration?

A 50-kg lawn mower has its rear wheels driven. When starting from rest on a level surface, the rear wheels spin. The coefficient of kinetic friction is 0.50. The normal force on the rear wheels is 314 N and on the front wheels is 176 N. What is the forward acceleration of the mower?

In Sample Problem 6/3, a 644-lb concrete block is being accelerated upward at 3.67 ft/sec^2. What is the tension T in the cable supporting the block? Use g = 32.2 ft/sec^2.

A 7.5-kg pendulum with its mass center at r = 0.25 m from pivot O is released from rest. Its moment of inertia about the pivot is IO = 0.650 kg-m^2. What is its initial angular acceleration (alpha) when released from the horizontal position (theta = 90 degrees)? Use g = 9.81 m/s^2.

In the equation for fixed-axis rotation, ΣMO = IOα, what does the term IO represent?

A uniform 20-kg slender bar of length 1.6 m is pivoted at one end O and released from rest in the horizontal position. What is the initial angular acceleration of the bar? Use g=9.81 m/s^2.

General plane motion of a rigid body can be analyzed as a combination of which two simpler types of motion?

A metal hoop (I_G = mr^2) is released from rest on an incline of 20 degrees. If it rolls without slipping, what is its linear acceleration `a` down the incline? Use g = 9.81 m/s^2.

In Sample Problem 6/7, a slender bar starts its motion from rest. Why is the normal component of the relative acceleration, (a_A/B)_n, equal to zero in the analysis?

In the analysis of a car door swinging open (Sample Problem 6/8), the moment equation about the hinge O is used. Why is this a good choice for the moment center?

What are the two distinct components that make up the total kinetic energy of a rigid body in general plane motion?

In the work-energy equation T1 + V1 + U'1-2 = T2 + V2, what forces' work must be accounted for in the potential energy terms, V1 and V2?

What is the primary advantage of using the impulse-momentum method for solving kinetics problems compared to the work-energy method?

According to the chapter review, which analysis method is indicated if the interval of motion is specified in terms of time rather than displacement?

What does the term 'unconstrained motion' imply about the accelerations of a rigid body?

In Sample Problem 6/15, a sheave and load system is analyzed using the impulse-momentum principle. The initial angular momentum about O is (HO)1 = -37.5 N-m-s, the angular impulse from t=0 to t=5s is 137.4 N-m-s, and the final angular momentum is (HO)2 = 11.72*omega2. What is the final angular velocity, omega2?

According to the chapter review, plane motion kinetics problems are approached in two main ways: Absolute-Motion Analysis and Relative-Motion Analysis. What does Relative-Motion Analysis use to solve problems?

The chapter review for kinetics outlines several principles and methods. Which kinetic method is most appropriate when a problem describes motion over an interval of displacement?

What is the key difference between constrained and unconstrained motion for a rigid body?

A uniform slender bar of mass m and length L is released from rest in a horizontal position. It is pivoted at a point O located at a distance L/4 from one end. What is its angular velocity, omega, when it passes through the vertical position?