Calculating Angular Acceleration w/ Torque & Moment of Inertia

In summary, when finding angular acceleration using torque and moment of inertia, the resulting units are in radians per second squared. The radian is a dimensionless unit that serves to distinguish a quantity as being angular in nature.
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Homework Statement



this is a question just to help with my understanding: ...

when Torque (kg m^2/s^2) and the Moment of Inertia (kg m^2) are known and used to find angular acceleration, ... T(net)/I, are the units for the resulting acceleration rad/s^2

Thanks :-)

Homework Equations


##\tau = I \alpha##

The Attempt at a Solution


[/B] Example:
t = 12 kg m^2/s^2
I = 3.00 kg m^2

angular acceleration = torque/I = 12 kg m^2/s^2 / 3.00 kg m^2 = 4 units(?) / s^2
 
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  • #2
Yes. Angular acceleration is given in radians per second squared ##(rad/s^2)##.

The radian is sort of a "unitless unit" that appears and disappears as required when working with angular quantities. It's based on a ratio of lengths from the unit circle, where an angle is defined via the arclength along the circle divided by the radius length. It serves to distinguish a quantity as being angular in nature.
 
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thank you! :-)
 
  • #4
gneill said:
unitless unit
How about "dimensionless unit"?
 
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haruspex said:
How about "dimensionless unit"?
Sure! That's probably better nomenclature. :smile:
 
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1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is measured in radians per second squared (rad/s^2).

2. How do you calculate angular acceleration?

Angular acceleration can be calculated by dividing the torque applied to an object by its moment of inertia. The formula is given by α = Σ/I, where α is the angular acceleration, Σ is the torque, and I is the moment of inertia.

3. What is torque?

Torque is the measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

4. What is moment of inertia?

Moment of inertia is the measure of an object's resistance to changes in its rotational motion. It is dependent on the object's mass, shape, and distribution of mass. The larger the moment of inertia, the more force is needed to cause the object to rotate.

5. How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the radius of rotation. The linear acceleration of a point on a rotating object is equal to the angular acceleration multiplied by the radius of rotation. This relationship is described by the equation a = αr, where a is the linear acceleration, α is the angular acceleration, and r is the radius of rotation.

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