The 4-kg rod AB is attached to a collar of negligible mass...

Name: Problem 43, Chapter 17: Vector Mechanics for Engineers: Statics and Dynamics
Uploaded: 2020-09-25T06:35:44-08:00
Duration: 15 min 8 s
Channel: Khoobchandra Agrawal
Description: The 4-kg rod AB is attached to a collar of negligible mass at A and to a flywheel at B. The flywheel has a mass of 16 kg and a radius of gyration of 180 mm. Knowing that in the position shown the angular velocity of the flywheel is 60 rpm clockwise, determine the velocity of the flywheel when point B is directly below C.

The 4-kg rod AB is attached to a collar of negligible mass at A and to a flywheel at B. The flywheel has a mass of 16 kg and a radius of gyration of 180 mm. Knowing that in the position shown the angular velocity of the flywheel is 60 rpm clockwise, determine the velocity of the flywheel when point B is directly below C.

Key Concepts

Moment of Inertia and Radius of Gyration

The moment of inertia is a measure of a body's resistance to rotational acceleration about an axis. It depends on how the mass is distributed relative to that axis. The radius of gyration is a related concept which provides a single distance value such that if all of the mass were concentrated at that distance from the axis, the body would have the same moment of inertia. Together, these concepts are fundamental in analyzing the rotational dynamics of a system where bodies rotate about an axis.

Angular Velocity

Angular velocity is the rate at which an object rotates, typically measured in radians per second or revolutions per minute. It is an essential concept in rotational dynamics since it links the motion of a rotating object to its kinetic energy. The conversion between angular motion and linear motion (through the relationship v = ?r) is key in solving problems that involve moving parts in a rotating system.

Rotational Kinetic Energy

Rotational kinetic energy quantifies the energy a rotating body possesses, analogous to translational kinetic energy in linear motion. It is given by the expression (1/2)I?², where I is the moment of inertia and ? is the angular velocity. This concept is usually employed alongside energy conservation principles to analyze systems undergoing rotational motion.

Conservation of Energy in Rotational Systems

Conservation of energy is a fundamental principle stating that energy cannot be created or destroyed but only transformed. In rotational dynamics, energy conservation is often applied by equating changes in potential energy to changes in rotational kinetic energy. This approach allows for the determination of unknown quantities such as angular velocity or speed of components in a system when the configuration changes.

Transcript

00:04 Hello everyone as shown in the figure of 4 kg rod ab and of length 720 millimeter that is 0 .72 meter attached to the collar having negligible mass at a and the flywheel be the mass of the flywheel is 16 kg and its radius of gyration is 180 m that is 0 .18 meter as shown in the figure at this position its angular velocity is 60 rpm or 2 pi radian per second in clockwise direction we have to calculate velocity of the flywheel when point v is directly below c this is c point i am marking with blue color so we have to find the velocity of flywheel when point v is directly below let us see here.

02:27 Moment of inertia of the rod a .v.

02:34 About its centroid will be 1 by 12 mass of a .v.

02:46 Calculating its value.

02:49 Mass is given 4 kg.

02:51 Length is 0 .72.

02:54 So it's a moment of inertia about its centroid would be 0 .1728 kg meter square.

03:17 Moment of inertia of the fly wheel.

03:27 Fly wheel we are marking fw or you can also mark ic.

03:34 So we can write mc.

03:38 It will be mc into k square.

03:45 Substitute the value.

03:47 Mass is given 16 kg.