Dimensional Analysis: Torque, Moment of Inertia & Angular Acceleration

In summary, dimensional analysis is a method used in physics to analyze relationships between different physical quantities, torque is a measure of rotational force, moment of inertia is a measure of resistance to changes in rotational motion, angular acceleration is the rate of change of angular velocity, and all three are related through Newton's second law for rotational motion.
  • #1
Mikealvarado100
55
0
Hi
The relation between torque, moment of inertia and angular acceleration is:
T=Ia
Have a look to it's units:
(N.m)=(kg.m^2).(Rad/s^2) >>>> N=kg.m.Rad/s^2
Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?
Thanks.
 
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  • #2
Mikealvarado100 said:
Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?
Starting with F = m⋅a, the dimensions give N = kg⋅m/s2. Insert this in your equation and remember that "Rad" is dimensionless (arc length/radius gives m/m).
 

1. What is dimensional analysis?

Dimensional analysis is a method used in physics to analyze and understand the relationships between different physical quantities. It involves examining the units of measurement associated with each quantity and using this information to derive the relationships between them.

2. What is torque?

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

3. How is moment of inertia calculated?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation.

4. What is angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is calculated by dividing the change in angular velocity by the change in time.

5. How are torque, moment of inertia, and angular acceleration related?

Torque, moment of inertia, and angular acceleration are all related through Newton's second law for rotational motion, which states that the net torque acting on an object is equal to the moment of inertia multiplied by the angular acceleration. In other words, the more torque applied to an object, the greater its angular acceleration will be, and the larger its moment of inertia, the slower its angular acceleration will be.

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