Engineering Mechanics: Dynamics Study (Book and Pearson eText)
14th Edition
ISBN: 9780134116990
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 21.6, Problem 76P
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The precession
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The rod AB has a mass of 20 kg，the mass of the piston A and B are both 5kg. Piston B is attached to a spring of constant k = 1200 N/m. The spring is un-stretched when θ = 0. If the rod is released from rest whenθ = 45°
Please find÷
(1) the moment inertia of the rod AB about its mass center G
(2)The angular velocity of rod AB at θ = 0°
(3）the velocity of piston A at θ = 0°
(4) the velocity of Piston B at θ = 0°
(hint: regard the piston A, B, rod as a system, during the motion, except the spring, the weight of rod AB, the weight of pistonB also does work). g = 9.8 m/s2
a rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm, 60 mm, 70 mm and 60 mm respectively. the 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 60°, 135° and 270° respectively measured clockwise from the first mass looking from this mass end of the shaft. the shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. determine, graphically or otherwise, the magnitudes of the masses and their respective angular positions.
An aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hour. The rotary engine and the propeller of the plane has a mass of 400 kg with a radius of gyration of 300 mm. The engine runs at 2400 r.p.m. clockwise, when viewed from the rear. Find the gyroscopic couple on the aircraft and state its effect on it. What will be the effect, if the aeroplane turns to its right instead of to the left ?
Chapter 21 Solutions
Engineering Mechanics: Dynamics Study (Book and Pearson eText)
Ch. 21.1 - Show that the sum of the moments of inertia of a...Ch. 21.1 - Determine the moment of inertia of the cone with...Ch. 21.1 - Determine moment of inertia Iy of the solid formed...Ch. 21.1 - Determine the moments of inertia Ix and Iy of the...Ch. 21.1 - The density of the material is . Express the...Ch. 21.1 - Prob. 6PCh. 21.1 - Prob. 7PCh. 21.1 - Prob. 8PCh. 21.1 - The weight of the cone is 15 lb, the height is h =...Ch. 21.1 - The density of the material is .
Ch. 21.1 - Prob. 11PCh. 21.1 - Determine the moment of inertia Ixx of the...Ch. 21.1 - Determine the product of inertia Iyz of the...Ch. 21.1 - Prob. 14PCh. 21.1 - Prob. 15PCh. 21.1 - Determine the moment of inertia of the rod about...Ch. 21.1 - Prob. 17PCh. 21.1 - Prob. 18PCh. 21.1 - Prob. 19PCh. 21.1 - Prob. 20PCh. 21.1 - Prob. 21PCh. 21.3 - If a body contains no planes of symmetry, the...Ch. 21.3 - Prob. 23PCh. 21.3 - Prob. 24PCh. 21.3 - The large gear has a mass of 5 kg and a radius of...Ch. 21.3 - Prob. 26PCh. 21.3 - Prob. 27PCh. 21.3 - Prob. 28PCh. 21.3 - Prob. 29PCh. 21.3 - Prob. 30PCh. 21.3 - Prob. 31PCh. 21.3 - Prob. 32PCh. 21.3 - The 20-kg sphere rotates about the axle with a...Ch. 21.3 - The 200-kg satellite has its center of mass at...Ch. 21.3 - Prob. 35PCh. 21.3 - Prob. 36PCh. 21.3 - Prob. 37PCh. 21.3 - Prob. 38PCh. 21.3 - Prob. 39PCh. 21.3 - Prob. 40PCh. 21.4 - Derive the scalar form of the rotational equation...Ch. 21.4 - Prob. 42PCh. 21.4 - Prob. 43PCh. 21.4 - Prob. 44PCh. 21.4 - The disk has a weight of 15 lb. Neglect the weight...Ch. 21.4 - Prob. 46PCh. 21.4 - Prob. 47PCh. 21.4 - Prob. 48PCh. 21.4 - Prob. 49PCh. 21.4 - Prob. 50PCh. 21.4 - Prob. 51PCh. 21.4 - The 5-kg circular disk is mounted off center on a...Ch. 21.4 - Prob. 53PCh. 21.4 - Prob. 54PCh. 21.4 - Prob. 55PCh. 21.4 - The 4-kg slender rod AB is pinned at A and held at...Ch. 21.4 - Prob. 57PCh. 21.4 - Prob. 58PCh. 21.4 - Prob. 59PCh. 21.4 - Show that the angular velocity of a body, in terms...Ch. 21.4 - Prob. 61PCh. 21.6 - The gyroscope consists of a uniform 450-g disk D...Ch. 21.6 - Prob. 63PCh. 21.6 - Prob. 64PCh. 21.6 - Prob. 65PCh. 21.6 - When viewed from the front of the airplane, the...Ch. 21.6 - Prob. 67PCh. 21.6 - Prob. 68PCh. 21.6 - Prob. 69PCh. 21.6 - Prob. 70PCh. 21.6 - Prob. 71PCh. 21.6 - Prob. 72PCh. 21.6 - Prob. 73PCh. 21.6 - Prob. 74PCh. 21.6 - Prob. 75PCh. 21.6 - Prob. 76PCh. 21.6 - Prob. 77PCh. 21.6 - Prob. 78P
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- An aeroplane makes a complete half circle of 70 metres radius, towards left, when flying at 500 km per hr. The rotary engine and the propeller of the plane has a mass of 600 kg and a radius of gyration of 0.3 m. The engine rotates at 2500 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.arrow_forwardA stepped cylinder has the dimensions R₁ = 0.30 m, R₂ = 0.65 m, and the radius of gyration, k, is 0.35 m. The mass of the stepped cylinder is 100 kg. Weights A and B are connected to the cylinder. If weight B has a mass of 80 kg, and weight A has a mass of 50 kg, how far does A move in 5 seconds? In which direction does it move? (Draw all FBDs)arrow_forwardA rotating shaft carries four unbalanced masses 20 kg, 16 kg, 18 kg and 14 kg at radii 55 mm, 65 mm, 75 mm and 65 mm respectively. The 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 65°, 135° and 270° respectively measured clockwise from the first mass.The shaft is dynamically balanced by two masses, both located at 55 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. Determine, balancing mass by drawing couple polygon and their respective angular position graphically.arrow_forward
- The turbine rotor of a ship has a mass of 2.2 tonnes and CO1(L2) rotates at 1800 rpm clockwise when viewed from the aft The radius of gyration of the rotor is 320 mm. Determine the gyroscopic couple and its effect when (a) The ship turns right at a radius of 250 m with a speed of 25 km/h. (b) The ship pitches with the bow rising at an angular velocity of 0.8 rad/s (c) The ship rolls at an angular velocity of 0.1 rad/s.arrow_forwardThe uniform 140-lblb beam is initially at rest when the forces are applied to the cables. Set FAFAF_A = 70 lblb and FBFBF_B = 190 lblb .(Figure 1) Determine the magnitude of the acceleration of the mass center at this instant. Determine the angular acceleration of the beam at this instant.arrow_forwardFind the resultant reaction at each bearing due to the mass and gyroscopic effects for a uniform disc of 8cm radius has a weight of 75N. It is mounted centrally in bearings which maintain its axle in a horizontal plane. The disc spins about it axle with a constant speed of 18 r.p.s. while the axle precesses uniformly about the vertical at 1.2 r.p.m. The directions of rotation you can assume in any direction If the distance between the bearings is 15cm.arrow_forward
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