Inertia - Basic Introduction, Torque, Angular Acceleration, Newton's Second Law, Rotational Motion

This video tutorial provides a basic introduction into inertia. Inertia is the property of an object to resist changes in its state of motion. According to Newton's First Law of motion, objects at rest tend to stay at rest and objects in motion tend to stay in motion unless acted on by a net external force. This video relates newton's second law of translational motion which is force equals mass times acceleration with newton's second law of rotational motion which is torque equals inertia times angular acceleration. This video provides the formula for rotational inertia of a hoop and a disk. The rotational inertia of an object depends not only on mass but the way that mass is distributed around a central axis of rotation. If the mass is distributed away from the central axis of rotation, the inertia of the object increases and there is more resistance to rotation. The general equation for the moment of inertia of a point in space is I=MR^2.
Intro to Rotational Motion:
• Rotational Motion Phys...
Angular Velocity:
• Angular Velocity Physi...
Angular Acceleration:
• Angular Acceleration P...
Rotational Kinematics:
• Rotational Kinematics ...
Intro to Torque:
• Torque, Basic Introduc...
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Parallel Axis Theorem:
• Parallel Axis Theorem ...
Rotational Dynamics:
• Rotational Dynamics - ...
Rotational Kinetic Energy:
• Rotational Kinetic Ene...
Rotational Power, Work, & Energy:
• Rotational Power, Work...
Work Done By a Constant Torque:
• Work Done By a Constan...
Angular Momentum & Torque:
• Angular Momentum - Bas...
_________________________________
What Is Angular Momentum?
• What Is Angular Momentum?
Angular Momentum Problems:
• Angular Momentum Physi...
Angular Impulse:
• Angular Impulse
Rotational Motion - Review:
• Torque, Moment of Iner...
Full-Length Videos and Worksheets:
/ collections
Physics PDF Worksheets:
www.video-tutor.net/physics-b...

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[@satyampandey2222]

I think you made a mistake there, in circular motion we talk about moment of inertia, which is different than just inertia Because if you compare the inertia of the disc and the ring it'll be same for both of them since they have the same mass, but the moment of inertia will be different for both of them

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Is the 1/2 an approximation? Wouldn't the fraction depend on the relative thickness of the disk?

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So is that angular acceleration rate in revolutions per second or radians per second?

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[@irvinglopes2489]

So my question is why is rotational inertia's coefficients 1/2,1, and 2/5. Are they just established coefficients? Will any rotating object without mass on the axis of rotation be 1 or MR^2, and will every object with mass on the axis of rotation be 1/2mr^2??

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[@carultch]

It comes from Calculus, and accounting for the distribution of mass. You can look up the derivations for common shapes of moment of inertia, like a solid uniform cylinder with a coefficient of 1/2, a solid uniform sphere with a coefficient of 2/5, and a thin uniform hoop with a coefficient of unity. The thin uniform hoop is a special case with the coefficient equal to unity, because all of the mass is concentrated at one radius from the axis of rotation.

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[@syedfarazali295]

PLEASE call it "ROTATIONAL INERTIA" or "MOMENT OF INERTIA" or "MASS MOMENT OF INERTIA" and not "Inertia". Inertia of both the objects is same because they have same mass and will posses the same tendency to resist any change in their state of motion and cannot be calculated using a formula.

[@ikkeennigij121]

I'm wondering, where does this constant come from when calculating inertia (e.g.: I=1Mr² for the hoop and I=1/2Mr² for the solid? is it something that's defined for certain shapes, if so what about custom shapes?

[@ikkeennigij121]

nvm, quick google search: basically for complex shapes you'd have to divide your shape into the available ones and then calculate them seperately to get the total inertia.

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very nice!!!! you forgot m/s^2 after a

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[@BrianBoruish]

Also, why is there a time component in some moments of inertia (lb*in*sec^2) and not in others (kg*m^2)?

[@carultch]

The reason lb-in-sec^2 has seconds in its units, has to do with correcting the pound unit to stop being a force unit, and be a mass unit instead. It is to get rid of the seconds that are in the denominator of the pound unit.

[@unknown-bx8my]

how can i calculate the inertia of a polygon?

[@user-zy8qo8xz9o]

4:50 if the total masses are equal then shouldnt they both have equal interia

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Which of the two will accelerate faster? T = I x alpha For solid disk I is smaller than hoop Means lower resistance to motion than hoop So Solid disk will roll down faster

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