Rate of Change of Angular Momentum Calculator

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✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖Final Angular Velocity of the particle.ⓘ Final Angular Velocity [ω_f]			+10% -10%
✖Initial angular velocity is the velocity at which motion starts.ⓘ Initial Angular Velocity [ω_o]			+10% -10%
✖Time Duration is what a clock reads, it is a scalar quantity.ⓘ Time Duration [t_rm]			+10% -10%

✖The Rate of Change of Angular Momentum is directly proportional to the external torque applied on the body.ⓘ Rate of Change of Angular Momentum [L_r]

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Formula

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Rate of Change of Angular Momentum

Formula

`"L"_{"r"} = ("I"*("ω"_{"f"}-"ω"_{"o"}))/"t"_{"rm"}`

Example

`"1.124516N*m"=("1.120kg·m²"*("45.125rad/s"-"14rad/s"))/"31s"`

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Rate of Change of Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration
L_r = (I*(ω_f-ω_o))/t_rm
This formula uses 5 Variables

Variables Used

Rate of Change of Angular Momentum - (Measured in Newton Meter) - The Rate of Change of Angular Momentum is directly proportional to the external torque applied on the body.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Final Angular Velocity - (Measured in Radian per Second) - Final Angular Velocity of the particle.
Initial Angular Velocity - (Measured in Radian per Second) - Initial angular velocity is the velocity at which motion starts.
Time Duration - (Measured in Second) - Time Duration is what a clock reads, it is a scalar quantity.

STEP 1: Convert Input(s) to Base Unit

Moment of Inertia: 1.12 Kilogram Square Meter --> 1.12 Kilogram Square Meter No Conversion Required
Final Angular Velocity: 45.125 Radian per Second --> 45.125 Radian per Second No Conversion Required
Initial Angular Velocity: 14 Radian per Second --> 14 Radian per Second No Conversion Required
Time Duration: 31 Second --> 31 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_r = (I*(ω_f-ω_o))/t_rm --> (1.12*(45.125-14))/31

Evaluating ... ...

L_r = 1.12451612903226

STEP 3: Convert Result to Output's Unit

1.12451612903226 Newton Meter --> No Conversion Required

FINAL ANSWER

1.12451612903226 ≈ 1.124516 Newton Meter <-- Rate of Change of Angular Momentum

(Calculation completed in 00.007 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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< 3 Rotary Motion Calculators

Rate of Change of Angular Momentum

Go Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration

Initial angular momentum

Go Initial Angular Momentum = Moment of Inertia*Initial Angular Velocity

Final angular momentum

Go Final Angular Momentum = Moment of Inertia*Final Angular Velocity

Rate of Change of Angular Momentum Formula

Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration
L_r = (I*(ω_f-ω_o))/t_rm

What is angular momentum?

Angular momentum is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity, which implies that here along with magnitude, the direction is also considered.

How to Calculate Rate of Change of Angular Momentum?

Rate of Change of Angular Momentum calculator uses Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration to calculate the Rate of Change of Angular Momentum, The Rate of Change of Angular Momentum formula is defined as The Product of Moment of Inertia and Difference of Final Angular Momentum, Initial Angular Momentum, Divided by Time. Rate of Change of Angular Momentum is denoted by L_r symbol.

How to calculate Rate of Change of Angular Momentum using this online calculator? To use this online calculator for Rate of Change of Angular Momentum, enter Moment of Inertia (I), Final Angular Velocity (ω_f), Initial Angular Velocity (ω_o) & Time Duration (t_rm) and hit the calculate button. Here is how the Rate of Change of Angular Momentum calculation can be explained with given input values -> 1.12 = (1.12*(45.125-14))/31.

FAQ

What is Rate of Change of Angular Momentum?

The Rate of Change of Angular Momentum formula is defined as The Product of Moment of Inertia and Difference of Final Angular Momentum, Initial Angular Momentum, Divided by Time and is represented as L_r = (I*(ω_f-ω_o))/t_rm or Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration. Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis, Final Angular Velocity of the particle, Initial angular velocity is the velocity at which motion starts & Time Duration is what a clock reads, it is a scalar quantity.

How to calculate Rate of Change of Angular Momentum?

The Rate of Change of Angular Momentum formula is defined as The Product of Moment of Inertia and Difference of Final Angular Momentum, Initial Angular Momentum, Divided by Time is calculated using Rate of Change of Angular Momentum = (Moment of Inertia*(Final Angular Velocity-Initial Angular Velocity))/Time Duration. To calculate Rate of Change of Angular Momentum, you need Moment of Inertia (I), Final Angular Velocity (ω_f), Initial Angular Velocity (ω_o) & Time Duration (t_rm). With our tool, you need to enter the respective value for Moment of Inertia, Final Angular Velocity, Initial Angular Velocity & Time Duration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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