(a) Explanation Given information: The length of slender rod is l . The weight of the rod is W . The mass of the rod is m . Calculation: Write the general equation of mass ( m ) of the rod. m = W g Here, g is the acceleration due to gravity. Write the equation of mass moment of inertia of rod. I = 1 12 m l 2 Sketch the initial and final position of the system as shown in Figure (1). Refer Figure (1), At initial position, the system is at rest. Therefore, the velocity ( v ¯ 1 ) , angular velocity ( ω 1 ) , and kinetic energy ( T 1 ) of the rod are zero. Write the equation of velocity ( v ¯ 2 ) at final position of the rod. v ¯ 2 = l 2 ω 2 Here, ω 2 is the angular velocity of rod at final position. Write the equation of kinetic energy ( T 2 ) of rod at final position. T 2 = 1 2 m v ¯ 2 2 + 1 2 I ω 2 2 Substitute l 2 ω 2 for v ¯ 2 and 1 12 m l 2 for I . T 2 = 1 2 m ( l 2 ω 2 ) 2 + 1 2 ( 1 12 m l 2 ) ω 2 2 = 1 8 m l 2 ω 2 2 + 1 24 m l 2 ω 2 2 = 1 6 m l 2 ω 2 2 Write the equation of work done ( U 1 → 2 ) of the system. U 1 → 2 = m g l 2 Apply the Principle of work and energy. T 1 + U 1 → 2 = T 2 Substitute 0 for T 1 , m g l 2 for U 1 → 2 , and 1 6 m l 2 ω 2 2 for T 2 (b) To determine The angular velocity and corresponding reaction at the pivot of the rod as it passes through a vertical position if W = 1.8 lb and l = 3 ft .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill 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 17.1, Problem 17.16P

(a)

To determine

Find the angular velocity of the rod as it passes through a vertical position.

Find the corresponding reaction at the pivot.

(b)

To determine

The angular velocity and corresponding reaction at the pivot of the rod as it passes through a vertical position if W=1.8 lb and l=3 ft.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.1, Problem 17.15P

Chapter 17.1, Problem 17.17P

Students have asked these similar questions

please solve this problem what the problem are asking to solve please explain step by step and give me the correct answer

please help me to solve this problem step by step

please help me to solve this problem and determine the stress for each point i like to be explained step by step with the correct answer

Chapter 17 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.2CQ Ch. 17.1 - Prob. 17.3CQ Ch. 17.1 - Prob. 17.4CQ Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Prob. 17.3P Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - Prob. 17.5P

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.

Find the angular velocity of the rod as it passes through a vertical position. Find the corresponding reaction at the pivot.