Explanation Given: Mass of the rod is m and length of the rod is L . Concept used: Expression for change of angular momentum is given as follows: H G = H x i + H y j + H z k ........ (1) Here, change in momentum is H G . Expression for rate of change of angular momentum is given as follows: H ˙ G = ( H ˙ G ) G x y z + ( Ω × H G ) ........ (2) Here, rate of change in momentum is H ˙ G . Calculation: Moment of inertia is calculated as follows: I x = I z = 1 12 m L 2 and I y = 0 Component of H G along x direction is calculated as follows: H x = I x ω 1 cos θ × sin θ H x = − 1 12 m L 2 ω 1 cos θ × sin θ Component of H G along y direction is calculated as follows: H y = I y ω y H y = 0 Component of H G along z direction is calculated as follows: H z = I z ω 2 H z = 1 12 m L 2 ω 2 Substitute − 1 12 m L 2 ω 1 cos θ × sin θ for H x , 0 for H y and 1 12 m L 2 ω 2 for H z in equation (1). H G = − 1 12 m L 2 ω 1 cos θ × sin θ i + 0 j + ( 1 12 m L 2 ω 2 ) k H G = − 1 24 m L 2 ω 1 sin 2 θ i + ( 1 12 m L 2 ω 2 ) k Angular velocity of the reference frame can be calculated as follows: Ω = ω x i + ω y j Ω = 0 i + ω 1 j Substitute − 1 24 m L 2 ω 1 ( 2 cos 2 θ ) i + ( 1 12 m L 2 ω 1 ) ( − 2 ω 2 cos θ sin θ ) j for ( H ˙ G ) G x y z and − 1 24 m L 2 ω 1 sin 2 θ i + ( 1 12 m L 2 ω 2 ) k for H G in equation (2) To determine (b) The couple M 2 . To determine (c) Dynamic reactions at C and D.

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 18.2, Problem 18.106P

To determine

(a)

The couple M1.

To determine

(b)

The couple M2.

To determine

(c)

Dynamic reactions at C and D.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.2, Problem 18.105P

Chapter 18.3, Problem 18.107P

Students have asked these similar questions

When the 18-kg wheel shown is attached to a balancing machine and made to spin at a rate of 12.5 rev/s, it is found that the forces exerted by the wheel on the machine are equivalent to a force-couple system consisting of a force F = (160 N)j applied at and a couple where the unit vectors form a triad that rotates with the wheel. (a ) Determine the distance from the axis of rotation to the mass center of the wheel and the products of inertia Ixy and Ixz (b) If only two corrective masses are to be used to balance the wheel statically and dynamically, what should these masses be and at which of the points A, B, D or E, should they be placed?

A thin disk of mass m = 4 kg rotates with an angular velocity w2 with respect to arm ABC, which itself rotates with an angular velocity w1 about the y axis. Knowing that w1 = 5 rad/s and w2 = 15 rad/s and that both are constant, determine the force-couple system representing the dynamic reaction at the support at A.

Q.5

Chapter 18 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

Ch. 18.1 - Prob. 18.1P 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 the...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Solve Prob. 18.6, assuming that the solid...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P

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.