Help me find angular acceleration?

Question

So I'm learning about torque in my physics class and in this problem we have to find angular acceleration. We're given that the torque applied to spin a wheel is 10 newton meters and the moment of inertia is .96 kilogram meter squared. I also know that the equation to find torque with angular acceleration and moment of inertia is τ = Iα (torque equals moment of inertia times angular acceleration). I plugged in the torque and moment of inertia, converted them to SI units, and divided the moment of inertia from the torque but I get 10 reciprocal second square (s^-2). Obviously that doesn't make sense because it needs to be radians per seconds squared. So what am I missing? I also need to convert it into degrees per seconds squared so if you want to convert it to that then go ahead.

Amy · Answer

You can think of radians as meters-per-meter-of-radius. For example, on a wheel spinning 3 rad/s, a point at radius 5m is moving at 15 m/s.

But being m/m makes the radian a dimensionless unit. Your analysis is correct, but rad/s^2 is the same dimensions as 1/s^2.

The equation τ = Iα specifically uses α in rad/s^2.

Stephen · Answer

A radian has no units. It is the ratio of 2 lengths: arc length to radius (of a sector of a circle).

So 1 rad.s⁻² is technically homogeneous to 1s⁻².
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τ = 10 N.m

Note that (because F=ma) 1N = 1kg.m.s⁻²
1Nm = 1kg.m².s⁻²

I = 0.96kg.m²

α = τ/I
.  .= (10kg.m².s⁻²) / (0.96kg.m²)
. .= 10.4s⁻²

This is more conventionally written as α = 10.4rad.s⁻² as it is more meaningful.

I have rounded to 3 significant figures in this case, as I think it is appropriate.

? · Answer

T = Iα
α = T/I = 10/0.96 = 10.4 rad/s² *

* N-m/kgm² = N/kgm = kg•m/s² ÷ kg•m = kg•m/s² x 1/kg•m   {kg cancels as does m leaving 1/s²}
1/s² = rad/s²  because rad isn't a unit in the normal sense of the word it is a unit-less RATIO.

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Help me find angular acceleration?

3 Answers