Angular Momentum and Mass Center

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  • Topic: Angular momentum, Rigid body, Moment of inertia
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ES 12: Dynamics of Rigid Bodies First Semester, 2012-2013

Due: October 5, 2012/ Class Hours PROBLEM SET FOR LQ4

Instructions: 1. Answer this problem set at the back page of used short/A4 size bond paper. 2. At the TOPMOST portion of the first page of your answer sheets, write the following: “I hereby certify that I have worked on this problem set by my own honest effort, without giving or receiving any inappropriate help. I understand that any evidence which contradicts the foregoing statement may be used against me, and I am prepared for the ensuing consequences thereof.” 3. Maximum of 2 problems per sheet. Show all relevant solutions neatly and state any assumptions used in solving. Box all final answers.

PROBLEM NO.1 In the crank piston system shown, a piston P is connected to a crank AB (b 16 cm.) by a 2 kg slender rod B ( l 40 cm.). The mass of the crank AB can be considered to be very small. During a test of the system, crank AB is made to rotate with a constant angular velocity of 60 rad/s clockwise. There is no force applied to the face of the piston. When 60the distance between points D and A , d, is 43.081 cm and the angle  of connecting rod BD from the horizontal is 30o. Consider this instant when 60, answer the following questions:



d

1.A) Show by kinematic analysis that the angular acceleration of connecting rod BD is 1328.5 rad/s2 1.B) Show by kinematic analysis that the acceleration of the mass center G of connecting rod BD has the horizontal and vertical components of acceleration aGx = 188.60 m/s2 and aGy = 249.42 m/s2; respectively. 1.C) Draw clearly the FBD = EFD diagram for the connecting rod BD. Label all points and vectors properly. 1.D) Determine the force acting at point B. 1.E) Determine both the horizontal and vertical components of the force acting on the bar BD at hinge D. PROBLEM NO.2 A uniform slender bar AB of mass m is suspended as shown from a uniform disk of the same mass m. Neglecting the effect of friction, determine the accelerations of points A and B immediately after a horizontal force P has been applied at B.

ES 12: Dynamics of Rigid Bodies First Semester, 2012-2013

Due: October 5, 2012/ Class Hours PROBLEM SET FOR LQ4

PROBLEM NO.3 A spring with stiffness k = 20 N/m is attached to the geometric center C of a5 kg homogenous disk as shown. The radius of the disk is 0.2 m. The disk is stationary and the spring is unstreched when a constant clockwise moment M = 50 N-mis applied to it. The disk rolls down without slipping down an inclined surface (β = 30°). Consider Position 1 when the disk is stationary and Position 2 when the disk’s geometric center has moved a distance of 0.6 m.

0.6 m Position 1

M C 0.2 m Position 2

β= 30°

3A) The work done on the disk by the applied constant moment from position 1 to position 2 is____. a. 30 J b. -30 J c. 150 J d. - 150 J 3B) The work done on the disk by the spring force from position 1 to position 2 is _______. a. 3.6 J b. -3.6 J c. 7.2 J d. - 7.2 J 3C) The work done on the disk by the force of gravity from position 1 to position 2 is ____. a. 29.43 J b. -29.43 J c. 14.72 J d. - 14.72 J 3D) Determine the total work done on the disk from position 1 to position 2. a. 175.83 J b. 55.83 J c. 157.52 J 3E) The kinetic energy of the disk at position 1 is _____. a. 10 J b. 20 J

d. 161.12 J

c. 30 J

d. zero d. 0.02 kg -m2

3F) The mass moment of inertia of the disk about its mass center C is______. a. 0.08kg -m2 b. 0.10 kg -m2 c. 0.20 kg -m2

3G) Determine the absolute velocity (magnitude and direction) of the disk’s mass center C at position 2. a. 42.90 m/s , to the right parallel to incline b. 6.55 m/s , to the right parallel to incline c. 14.89 m/s , to the right parallel to incline d. 3.86 m/s , to the right parallel to incline

ES 12: Dynamics of Rigid Bodies First Semester, 2012-2013

Due: October 5, 2012/ Class Hours PROBLEM SET FOR LQ4

PROBLEM NO.4 An eccentric cylinder of...
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