(a) Explanation Given information: The side ( a ) of the square is 225 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: 9781260265453

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 18.86P

(a)

To determine

The constant angle β that the plate forms with the horizontal x-axis when ω=12 rad/s.

(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 18.85P

Chapter 18.2, Problem 18.87P

Students have asked these similar questions

Qu 3 Nickel (Ni) single crystal turbine blades burn less fuel at higher temperatures because blades are grown on [110] closed packed direction. Nickel (Ni) at 20°C is FCC, and has an atomic radius, R, of 0.125 nm. Draw a reduced-sphere unit cell for this crystal and draw and label the vector [I 10], starting from the origin (0, 0, 0). a) Calculate the length of the vector [| 10] in nanometers. Express your answer in nanometers to one significant figure. b) Calculate the linear density of Nickel in the [| 1 0] direction in [atom/nm]. Express your answer in atoms/nm to one significant figure. show all work problems

handwritten-solutions, please!

Chapter 18 Solutions

VECTOR MECH...,STAT.+DYN.(LL)-W/ACCESS

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 constant angle β that the plate forms with the horizontal x -axis when ω = 12 rad/s .

Solution Summary: The author calculates the constant angle beta that the plate forms with the horizontal x -axis.