(a) Explanation Given information: The side ( a ) of the square is 300 mm. The constant angular velocity ( ω ) of the clevis is 12 rad/s. Calculation: Let point O be the midpoint of axle AB and consider principal axes x ′ , y ′ , and z ′ with origin at point O . Sketch the axes of the system as shown in Figure (1). Refer Figure (1), Write the equation of the mass moment of inertia about x ′ -axis. I x ′ = 1 12 m a 2 Write the equation of the mass moment of inertia about z ′ -axis. I z ′ = 1 3 m a 2 Find the principal moment of inertia about y ′ -axis using the equation: I y ′ = I x ′ + I z ′ Substitute 1 12 m a 2 for I x ′ and 1 3 m a 2 for I z ′ . I y ′ = 1 12 m a 2 + 1 3 m a 2 = 5 12 m a 2 Write the vector form of angular velocity ( ω ) of the system. ω = − ω sin β i ′ + ω cos β j ′ Write the equation of angular momentum ( H O ) about point O . H O = I x ′ ω x ′ i + I y ′ ω y ′ j + I z ω z k (1) Substitute − ω sin β i ′ for ω x ′ i , ω cos β j ′ for ω y ′ j , and 0 for ω z . H O = I x ′ ( − ω sin β i ′ ) + I y ′ ( ω cos β j ′ ) + I z ( 0 ) k = − I x ′ ω sin β i ′ + I y ′ ω cos β j ′ Write the angular velocity of reference frame ( Ω ) . Ω = ω Substitute − ω sin β i ′ + ω cos β j ′ for ω . Ω = − ω sin β i ′ + ω cos β j ′ The rate of change of angular momentum ( H ˙ O ) O x y z about the reference frame is 0. Because the reference frame rotating about fixed point O . Write the equation of rate of change of angular momentum ( H ˙ O ) of the system. H ˙ O = ( H ˙ O ) O x y z + Ω × H O Substitute 0 for ( H ˙ O ) O x y z , − ω sin β i ′ + ω cos β j ′ for Ω , and − I x ′ ω sin β i ′ + I y ′ ω cos β j ′ for H O (b) To determine The largest value of angular velocity ( ω ) for which the plate remains vertical.

12th Edition

ISBN: 9781260804638

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 18.2, Problem 18.87P

(a)

To determine

The value of angular velocity (ω) for which the plate forms a constant angle β=60° with the horizontal x-axis.

(b)

To determine

The largest value of angular velocity (ω) for which the plate remains vertical.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.2, Problem 18.86P

Chapter 18.2, Problem 18.88P

Students have asked these similar questions

الثانية Babakt Momentum equation for Boundary Layer S SS -Txfriction dray Momentum equation for Boundary Layer What laws are important for resolving issues 2 How to draw. 3 What's Point about this.

R αι g The system given on the left, consists of three pulleys and the depicted vertical ropes. Given: ri J₁, m1 R = 2r; απ r2, J2, m₂ m1; m2; M3 J1 J2 J3 J3, m3 a) Determine the radii 2 and 3.

B: Solid rotating shaft used in the boat with high speed shown in Figure. The amount of power transmitted at the greatest torque is 224 kW with 130 r.p.m. Used DE-Goodman theory to determine the shaft diameter. Take the shaft material is annealed AISI 1030, the endurance limit of 18.86 kpsi and a factor of safety 1. Which criterion is more conservative? Note: all dimensions in mm. 1 AA Motor 300 Thrust Bearing Sprocket 100 9750 เอ

Chapter 18 Solutions

VECTOR MECHANICS FOR ENGINEERS W/CON >B

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - Prob. 18.3P Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - A homogeneous disk of mass m = 8 kg rotates at the...Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Determine the angular momentum HO of the disk of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The value of angular velocity ( ω ) for which the plate forms a constant angle β = 60 ° with the horizontal x -axis.

Solution Summary: The author calculates the angular velocity and the mass moment of inertia using the following equations.