PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 21, Problem 23P
To determine
Show that if the angular momentum of a body is determined with respect to an arbitrary point, then
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The 100-kg beam BD shown in Fig.17-13a is supported by two rods
having negligible mass. Determine the force developed in each rod if
at the instant = 30°, w = 6 rad/s.
A
0.5 m
-0 = 30°
B
0.4 m-
co
G
0.4 m
n
(G) ►
(ac)₁
TB 30°
30°
4
0.4 m
-0.4 m
981 N
TD 30°
(b)
Alo
0.5 m
al
α
(c)
w = 6 rad/s
a
B
Q-4) The rod, having a weight of
16N and a length of 2.5m,
contains a joint at O which is 0.5m
distant from point B. The other
end of the rod is attached to a
2,5 m-
0,5 m
spring that is compressed by 4cm
A
with
Ks= 250N/cm. At this
moment the rod is horizontal.
When released; calculate it's
angular velocity (passing by the
vertical position) and reaction
forces at the joint 0.
The 21-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.5
m. If it is subjected to the constant moment M = 78 N·m and is released from rest
from the position as shown, determine its angular velocity W (in rad/s) when it has
rotated 45°. Please pay attention: the numbers may change since they are
randomized. Your answer must include 2 places after the decimal point. Take g =
9.81 m/s².
L
Your Answer:
Answer
Chapter 21 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 21 - Show that the sum of the moments of inertia of a...Ch. 21 - Prob. 2PCh. 21 - Prob. 3PCh. 21 - Determine the moments of inertia Ix and Iy of the...Ch. 21 - Prob. 5PCh. 21 - Determine by direct integration the product of...Ch. 21 - Prob. 9PCh. 21 - Prob. 10PCh. 21 - Determine the moment of inertia Ixx of the...Ch. 21 - Prob. 13P
Ch. 21 - Prob. 14PCh. 21 - Prob. 15PCh. 21 - The bent rod has a weight of 1.5 lb/ft. Locate the...Ch. 21 - If a body contains no planes of symmetry, the...Ch. 21 - Prob. 23PCh. 21 - Prob. 25PCh. 21 - Prob. 28PCh. 21 - Prob. 29PCh. 21 - Prob. 30PCh. 21 - The 2-kg thin disk is connected to the slender rod...Ch. 21 - Prob. 33PCh. 21 - Prob. 36PCh. 21 - Prob. 37PCh. 21 - Prob. 40PCh. 21 - Prob. 41PCh. 21 - Prob. 42PCh. 21 - Prob. 48PCh. 21 - Prob. 51PCh. 21 - Prob. 54PCh. 21 - Show that the angular velocity of a body, in terms...Ch. 21 - A thin rod is initially coincident with the Z axis...Ch. 21 - The top consists of a thin disk that has a weight...Ch. 21 - Prob. 66PCh. 21 - Prob. 69PCh. 21 - Prob. 70PCh. 21 - Prob. 73PCh. 21 - Prob. 74PCh. 21 - Prob. 77P
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- The 23-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.3 m. If it is subjected to the constant moment M = 82 N·m and is released from rest from the position as shown, determine its angular velocity W (in rad/s) when it has rotated 45 Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: Answerarrow_forward*13=108. The collar, which has a weight of 3 lb, slides along the smooth rod lying in the horizontal plane and having the shape of a parabola r = 4/(1 – cos 0), where 0 is in radians and r is in feet. If the collar's angular rate is constant and equals ò = 4 rad/s, determine the tangential retarding force P needed to cause the motion and the normal force that the collar exerts on the rod at the instant 0 = 90°.arrow_forwardThe bus is driven from the flywheel having inertia J = 20 kgm2. How long distance can pass the bus from the energy stored in the flywheel if its angular velocity is ω = 1800 rad/s and the power needed for bus moving with speed v = 30 km/h is 60 kW?.arrow_forward
- The 21-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.5 m. If it is subjected to the constant moment M = 78 N•m and is released from rest from the position as shown, determine its angular velocity w (in rad/s) when it has rotated 45°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s2. `L MV Your Answer: Answerarrow_forward3. The pendulum consists of a 10-kg uniform disk and a 3-kg uniform slender rod. Determine the kinetic energy at this instant if the pendulum has an angular velocity of 5 rad/s clockwise. B 0.8 m *M = 30 N ·m -2 m-arrow_forwardThe wheel has a mass of 100 kg and a radius of gyration of ko = 0.2 m. A motor supplies a torque M = (400 + 900) N/m, where 0 is in radians, about the drive shaft at O. Determine the total work done on the system (in kJ) after the loading car travels s = 2.0 m. The mass of the car is 280 kg and initially it is at rest when = 0 and 0 = 0°. Neglect the mass of the attached cable and the mass of the car's wheels. = 30° M 0.3 marrow_forward
- A helicopter is moving at an inertial speed of vo = 10 m/s while its rotor blades spin at w = 40 rad/s CCW. Consider a body frame B = {G, 6₁, 6₂, 6₂} that is located at the rotor hub and has ₁ axis aligned and rotating with one of the blades. The tip of another blade is located at position P with respect to the body frame, that is, rp/G = 3 b₁ + 3 b2 meters. 1. What is the inertial velocity Tvp/o of P with respect to O in frame I? Express your answer in terms of the unit vectors of frame I. Assume 0 = 15 deg. ხე. i3 22 i3 b1 i₁ 2. Now suppose that at the same instant as in Part A the rotor blade experiences a failure from a bird strike and a segment of the blade at P brakes off and is flung away from the helicopter at a body-relative speed Bvp/G = 20 6₂ m/s. What is the inertial velocity Tvp/o of P with respect to O in frame I? Express your answer in terms of the unit vectors of frame I. Bup/G b2 VO VOarrow_forwardWhen the angle θ = 90 °, the cylinder BE starts with a vertical force (F = 3210 N) Newtons on the platform. Also, the box (box) is 200 kg and the angular velocity (ω) of body AB is 9 (rad / s). First, treat the box and platform as a single body to find the following: The magnitude of the reaction forces at points B and D. Box aG acceleration in the x and y direction. Second, having progressed earlier, only found the following for the platform: Reaction force from the box on the platform. Minimum symbol minimum A request of the consonant (μs) to disallow the box.arrow_forwardRod OA rotates counterclockwise at a constant angular rate θ˙ = 4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r=(1.6cosθ)m. Both collars have a mass of 0.55 kg . Motion is in the horizontal plane. Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant θ = 45∘ Determine the magnitude of the force that OA exerts on the other collar at the instant θ = 45∘arrow_forward
- Maya's team has designed a wheelchair for elderly, which has a wheel with a mass of 25 kg and a radius of gyration kß = 0.15 m. The wheel is initially spinning at w = 40 rad/s. The task is to determine the time required for the wheel's motion to come to a stop after being placed on the ground, considering the coefficient of kinetic friction µc =0.5 and assuming that there are no additional weights on the wheelchair themselves. Additionally, the students must calculate the horizontal and vertical components of the reaction that the pin at point A exerts on AB during this time. Neglect the mass of AB. A -0.4 m 0.2 m В MORB C 0.3 m ωarrow_forwardWhen in the mode of adsorbing, the vertical shaft is rotating with an angular velocity of 3 rad/s at 0 = 0°. When picking up trashes, a force F needs to be applied to the collar so that 0 = 90°. Help students determine the angular velocity of the shaft at 0 = 90°. Also, find the work done by force F from 0 = 0° to 0 = 90°. Neglect the mass of rods GH and EF and the collars I and J. The rods AB and CD each have a mass of 10 kg. 0.3 m E 0.3 m 0.1 m 0.3 m A 0.1 m H F 0 0.3 m Barrow_forwardAs in the figure, in an amusement vehicle rotating in the amusement park, the center shaft rotates at a speed of n=9 rpm. Meanwhile, the child is moved with the position equations r = (2 sinθ + 5) m and z = (3 cosθ) m. Find the forces generated in the child in all three axes (r, θ, z). The weight of the child is m = 31 kg. θ=115 degrees at the time the photo was taken.arrow_forward
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