# Angular velocity and acceleration

1. Jun 19, 2004

### Kreativitie

Hey i have this problem and would like to know if what i got is somewhere in the right direction. Any help would be GREATLY appreciated

A gymnast is performing a forward double somersault.

The gymnast’s initial angular velocity is 0 rad/s.
The gymnast generates a 115 N-m torque.
The torque is applied to the gymnast’s body for 0.22 s.
In the layout position, the gymnast’s moment of inertia is 11.4 kg-m2

What is her angular acceleration and her final angular velocity (during layout position)?

Heres what i got

Angular acceleration
T=Iα

115 Nm=11.4 kg-m2(α)
115 Nm/11.4 kg-m2 = 11.4 kg-m2(α)/ 11.4 kg-m2 =10.08 kg-m2

Angular velocity (w)
Tt=I(w)

104 Nm (.22s) = 11.4kg-m2(w)
104Nm(.22s) / 11.4kg-m2 = 11.4kg-m2(w) / 11.4kg-m2 = 2.22 kg-m2

2. Jun 19, 2004

### arildno

You seem to know which equations you should use, but you must develop a clearer notation:
"115 Nm=11.4 kg-m2(α)
115 Nm/11.4 kg-m2 = 11.4 kg-m2(α)/ 11.4 kg-m2"

Your second line equaltiy is certainly consistent with your first line equality; i.e, your doing correct maths.

However, when writing units, "kg-m2" is very cryptic; write instead kg*m^2
(Or:$$kg*m^{2}$$)

Your continued equality has wrong units, apart from being a very unfortunate way of notation:

We know that:$$Nm=\frac{kg*m^{2}}{s^{2}}$$
Hence:$$\frac{Nm}{kg*m^{2}}=\frac{1}{s^{2}}$$
Surely, this is the unit of angular acceleration!
In order to make a clearer notation, this is an example:
$$115Nm=11.4kg*m^{2}\alpha$$
$$\alpha=\frac{115}{11.4}\frac{Nm}{kg*m^{2}}=10.08s^{-2}$$

Why have you suddenly changed 115 into 104 in your equation for the angular velocity?
You end up with wrong units again, and you must work on your notations.