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December 28th, 2016, 10:40 PM   #1
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Trouble comparing angular acceleration to linear acceleration :

I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration to linear acceleration.

Looking at each equation, they are not as similar as some of the other equations are:

1. Anglular acceleration = velocity squared / radius
2. Linear acceleration = force/ mass

I would think angular acceleration would take torque into consideration. How is Vsquared similar in relation to force, and how is radius's relation to Vsquared match the relationship between mass and force?
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December 29th, 2016, 08:18 AM   #2
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Quote:
1. Anglular acceleration = velocity squared / radius
your #1 equation is incorrect ... angular acceleration, $\alpha = \dfrac{\tau}{I}$, where $\tau$ is the net torque and $I$ is the rotational inertia. Also, $\alpha = \dfrac{a_T}{r}$, where $a_T$ is tangential acceleration (one component of linear acceleration) and $r$, of course, is radius.

The other component of linear acceleration is centripetal acceleration, $a_c = \dfrac{v^2}{r}$.
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December 29th, 2016, 10:56 PM   #3
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Quote:
Originally Posted by SophiaRivera007 View Post
I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration to linear acceleration.

Looking at each equation, they are not as similar as some of the other equations are:

1. Angular acceleration = velocity squared / radius
2. Linear acceleration = force/ mass

I would think angular acceleration would take torque into consideration. How is Vsquared similar in relation to force, and how is radius's relation to Vsquared match the relationship between mass and force?
Angular acceleration = velocity squared / radius. It's the magnitude of the linear acceleration towards the centre of an object following a circular path at constant angular velocity. Angular acceleration is the derivative of angular velocity, and the analogue of Newton's second law is that angular acceleration equals torque divided by moment of inertia.

In simple words, angular acceleration is the rate of change of angular velocity, which further is the rate of change of the angle θ.

This is very similar to how the linear acceleration is defined.

a=d^2x/dt^2→α=d^2θ/dt^2

Like the linear acceleration is F/m, the angular acceleration is indeed τ/I, τ being the torque and I being moment of inertia (equivalent to mass).

And Let me solve your confusion:

The tangential velocity in case of a body moving with constant speed in a circle is same as its ordinary speed. The name comes from the fact that this speed is along the tangent to the circle (the path of motion for the body). Its magnitude is equal to the rate at which it moves along the circle. Geometrically you can show that v=rω.

Last edited by skipjack; December 30th, 2016 at 09:36 AM.
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