Angular velocity and acceleration

[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

 

[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.

 

[M98Ranger]

/s

Based on the given information, your calculations seem to be in the right direction. However, there are some things that can be improved upon. Let's break down the problem and see where we can make some adjustments.

First, we know that the gymnast's initial angular velocity is 0 rad/s. This means that she starts from rest and has no initial rotational motion. Next, we are given the torque applied to her body, which is 115 N-m. This torque is responsible for causing the gymnast's angular acceleration. So, we can use the formula T = Iα to calculate the angular acceleration, where T is the torque, I is the moment of inertia, and α is the angular acceleration.

Plugging in the given values, we get:

115 N-m = 11.4 kg-m2(α)

Rearranging the equation to solve for α, we get:

α = 115 N-m / 11.4 kg-m2 = 10.08 rad/s2

This is the angular acceleration of the gymnast during the 0.22 seconds that the torque is applied.

Next, we can use the formula ω = ω0 + αt to calculate the final angular velocity (ω) of the gymnast at the end of the 0.22 seconds. Here, ω0 is the initial angular velocity (which is 0 rad/s), α is the angular acceleration we just calculated, and t is the time (0.22 seconds).

Plugging in the values, we get:

ω = 0 + (10.08 rad/s2)(0.22 s) = 2.22 rad/s

So, the final angular velocity of the gymnast during the layout position is 2.22 rad/s.

In summary, your calculations were mostly correct, but there were some minor errors in the units and equations used. By following the correct formulas and units, you can ensure that your calculations are accurate and in the right direction. Keep up the good work!