[SOLVED] What is the Units of Mi and T in the equation T = Mi X acc?

[abhi@eda]

What is the Unit of Moment of Inertia in the Torque Equation T = Mi X Acceleration?

and what will be the Unit of resulting torque value?


for example.if the Mi = 33Nm^2 ( 3.37 Kg.meter^2) and the Acceleration is 17.46 rads/sec^2..

the SI unit of Mi is kg.m^2

then if kg.m^2 is used,its T=3.37kg.m^2 X 17.48 rads/sec^2 = 58.84 Nm or 58.84kg.m?[am confused here!]

what value is used for Mi , Nm^2 or Kg.meter^2?

and what will be the unit of the resulting torque value?

i searched and found out the Mi's SI unit is kg.m² and in the place where i looked, kg.m² is used in Torque equation.. but the Torque t is in Nm Unit,shouldn't it be in unit kg.m ??

how is it possible?

please explain me.

 

[godfreyl]

the SI unit of Mi is kg.m^2

Yes, that's correct.

what value is used for Mi , Nm^2 or Kg.meter^2?

Kg.meter^2
erikl and I both got that wrong in your previous thread. Sorry.

in the place where i looked, kg.m² is used in Torque equation.. but the Torque t is in Nm Unit

That's correct.

shouldn't it be in unit kg.m ??

No, the unit of totque is Nm.

For the equation T = Mi * Acceleration, the units work like this:

Unit for Mi = kg.m^2
Unit for angular acceleration = rad/s^2

So the unit for torque
= kg.m^2 * rad/s^2
= kg * m *m * rad / s^2
= rad * kg * m * m / s^2
= rad * m * kg * m / s^2
= rad * m * N (because N = kg * m / s^2)
=> m * N or N.m (because radians are dimensionless, so you can divide a value with unit rad * m * N by 2*pi to get the answer in unit Nm)

-------------------------------------------------

Also, be very careful about converting between Kg and Newtons. For example, you wrote:

Mi = 33Nm^2 ( 3.37 Kg.meter^2)

That's just plain wrong.

I guess you got that idea because 3.37Kg * 9.98m/s^2 = 33N.

Earth's gravity is 9.98m/s^2 but Earth's gravity has got nothing to do with your calculations.

What you're interested in is the angular acceleration of the blades around the axis, not how fast the blades would accelerate down towards the ground if the axle broke and they fell off.

--------------------------------

Edit: Oops I made a typo. Fixed now. Note it's divide not multiply in bold above.

 

[abhi@eda]

Yes, that's correct.


Kg.meter^2
erikl and I both got that wrong in your previous thread. Sorry.


That's correct.


No, the unit of totque is Nm.

For the equation T = Mi * Acceleration, the units work like this:

Unit for Mi = kg.m^2
Unit for angular acceleration = rad/s^2

So the unit for torque
= kg.m^2 * rad/s^2
= kg * m *m * rad / s^2
= rad * kg * m * m / s^2
= rad * m * kg * m / s^2
= rad * m * N (because N = kg * m / s^2)
=> m * N or N.m (because radians are dimensionless, so you can divide a value with unit rad * m * N by 2*pi to get the answer in unit Nm)

-------------------------------------------------

Also, be very careful about converting between Kg and Newtons. For example, you wrote:

That's just plain wrong.

I guess you got that idea because 3.37Kg * 9.98m/s^2 = 33N.

Earth's gravity is 9.98m/s^2 but Earth's gravity has got nothing to do with your calculations.

What you're interested in is the angular acceleration of the blades around the axis, not how fast the blades would accelerate down towards the ground if the axle broke and they fell off.

--------------------------------

Edit: Oops I made a typo. Fixed now. Note it's divide not multiply in bold above.

thank you godfreyl,thats cleared some of my doubts,thank you very much