If in Prob. 43 the angular velocity of the flywheel is to be the same in the position shown and

If in Prob. 43 the angular velocity of the flywheel is to be...

Key Concepts

Angular Velocity

This concept refers to the rate at which an object rotates around an axis. It quantifies how fast the object is spinning and is typically measured in radians per second. Understanding angular velocity is essential when analyzing rotational motion because it provides a measure of the instantaneous rate of rotation at any given position.

Rotational Kinematics

Rotational kinematics is the part of mechanics that deals with the motion of bodies rotating about an axis. It involves the study of angular displacement, angular velocity, and angular acceleration, and it uses equations analogous to linear kinematics. This area is key when determining dynamic behavior in different positions of rotating systems.

Conservation of Angular Momentum

The principle of conservation of angular momentum states that if no external torques act on a system, its total angular momentum remains constant. This is particularly important in problems where a system transitions between different configurations while maintaining the same overall spin characteristics, allowing for the prediction of angular velocities in various positions.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion about an axis. It depends on how the mass of the object is distributed relative to the axis of rotation. In many rotational dynamics problems, changes in the configuration of a system alter the moment of inertia, influencing the angular velocity if angular momentum is conserved.

Transcript

00:01 Hello friends as shown in the figure a rod av of mass 4 kg and length 720 millimeters that is 0 .72 meter attached to the color of negligible mass at a and to the fly wheel at position v mass of the flywheel is 16 kg and its radius is given sorry radius of variation is 1 that is 0 .18 meter and a radius of the way is 240 mm that is 0 .24 in the given position and when point b is directly above c angular velocity is same we have to point the angular velocity so we have to calculate omega for omega 1 is called to omega 2 omega 1 is angular velocity in position soar and omega 2 when b point just velocity moment of the rod a v about its center of mass 1 by 12 mass of av into and a v square substituting the value mass of rod av is 4 kg length is 0 .72 meter.

02:36 So we will get moment of inertia of the rod about its center of mass.

02:44 01728 kgmeter square.

02:50 Moment of inertia of the flywheel mc into kh square.

02:57 Mass is 16 kg.

02:59 Radius of variation is 0 .18.

03:02 So its value will be 0 .514 sorry 0 .5184 kg meter is.

03:16 Square now see the initial position is the v c point this is the position of b point this is the a say this angle is beta this is the velocity of a this will be the velocity of center of mass v war this is the velocity of a v this is center of mass cg so center of mass is h1 meter above the center of the wheel.

04:35 So for position, one as soren figure, omega is equal to omega 1 in clockwise direction.

04:49 Sign of beta is equal to 0 .24 upon 0 .72.

04:55 So it will be 19 .471 degree.

05:01 Height of center of mass of the rod, av, above the center of v, half of 0 .72.

05:12 Of meter so it would be 0 .33941 meter and gravitational potential energy mav into g h1 4 into 9 .81 h1 already we have calculated so this gravitational potential energy at this position is 13 .318 .385 jules now we will analyze kinematics.

06:04 Velacity of v, point will be, r into omega 1, that is 0 .24 omega 1.

06:20 Angular velocity of rod ab will be 0 and velocity of center of mass will be equal to velocity of v.

06:35 So total kinetic energy at this position, kinetic energy of translatory motion, kinetic energy of rotational motion, and kinetic energy of rotation of the v.

07:03 Substituting the value, mass of rod a .v is 4kg.

07:08 Its velocity is 0 .24 times omega.

07:16 Omega a .v .0.

07:20 I see we have calculated 0 .5184 omega 1 square...

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