(a) Explanation Given information: The angular velocity is ω . The angular momentum is H O . The kinetic energy of the rigid body is T . Calculation: The expression for the angular momentum of the rigid body as follows: H O = ( I x ω x − I x y ω y − I x z ω z ) i + ( − I x y ω x + I y ω y − I y z ω z ) j + ( − I x z ω x − I y z ω y + I z ω z ) k The expression for the angular velocity of the rigid body as follows: ω = ω x i + ω y j + ω z k Calculate the dot product of angular momentum and angular velocity using the relation: Dot product = H O ⋅ ω Substitute ( I x ω x − I x y ω y − I x z ω z ) i + ( − I x y ω x + I y ω y − I y z ω z ) j + ( − I x z ω x − I y z ω y + I z ω z ) k for H O and ω x i + ω y j + ω z k for ω . H O ⋅ ω = [ ( I x ω x − I x y ω y − I x z ω z ) i + ( − I x y ω x + I y ω y − I y z ω z ) j + ( − (b) To determine Show that the angle ( θ ) between ω and H O will always be acute.

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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 18.1, Problem 18.37P

(a)

To determine

Prove that HO⋅ω=2T.

(b)

To determine

Show that the angle (θ) between ω and HO will always be acute.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.1, Problem 18.34P

Chapter 18.1, Problem 18.38P

Students have asked these similar questions

Four masses A, B, C and D are attached to a shaft and revolve in the same plane. The masses are 24 kg, 20 kg, 21 kg, and 18 kg, respectively and their radii of rotations are 50 cm, 50 cm, 60 cm and 30 cm. the angular position of the masses B, C, and D are 60º, 135º and 270º from the mass A. the shaft is rotating with a constant angular speed ω = 500 rpm. We need to find : 1. The magnitude and direction of the resultant inertia force before balancing 2. The magnitude and direction of the balancing mass at a radius of 10 cm The magnitude of the resultant force, in Newton, before balancing is = The direction of resultant force before balancing measured in degree CCW from the mass A is = The magnitude of the balancing mass in kg is = The direction of the balancing mass measured in degree CCW from the mass A is = the magnitude of resultant force after balancing is =

Rod 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 0.7 kg . Motion is in the horizontal plane. (Figure 1)

Rod OA rotates counterclockwise at a constant angular rate 0-4 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= (1.6 cos 6) m. Both collars have a mass of 0.65 kg. Motion is in the vertical plane. (Figure 1) Figure r=1.6 cos 9. 0-4 rad/s 0.8 m 1 of 1 Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant 0=45 Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) F= Value Submit μÁ Part B Previous Answers Units X Incorrect; Try Again; 5 attempts remaining Determine the magnitude of the force that OA exerts on the other colar at the instant @-45. Express your answer to three significant figures and include the appropriate units. View Available Hint(s)

Chapter 18 Solutions

VECTOR MECHANIC

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.

Prove that H O ⋅ ω = 2 T .

Solution Summary: The author proves that H_Ocdotomega =2T. The angular momentum and kinetic energy of the rigid body are T.