Net Torque of CD: Calculating with Mass & Radius

[elemnt55]

A CD has a mass of 18.0 g and a radius of 6.11 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 19.6 rad/s in 0.768 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

Formula I am using: .5MR^2 for the I which = 25.5208
Then the w= chg in radians/ chg in time
Then the a = chg in w/ chg in time

Net torque = Ia

so i get 1827.33J which isn't right

i also tried converting the g into kg and the cm into m but got wrong answer

 

[Doc Al]

Formula I am using: .5MR^2 for the I which = 25.5208

25.52 rad/sec^2 is the angular acceleration, not the rotational inertia.

What did you calculate for I? (Yes, convert to standard units: kg & m)

 

[thepatientmental]

First of all, it is commendable that you are using the correct formula for the moment of inertia (I) of a uniform solid disk, which is 0.5MR^2. However, there are a few errors in your calculation.

Firstly, you have used the incorrect value for the mass of the CD. The given value is 18.0 g, but you have used 18.0 kg. This results in a much larger moment of inertia, which leads to a higher net torque value.

Secondly, you have not converted the radius from centimeters to meters. The correct radius to use in the formula is 0.0611 m, not 6.11 m. This also contributes to the higher net torque value you have calculated.

To get the correct answer, you need to use the correct values for mass (0.018 kg) and radius (0.0611 m) in the formula. This will give you a moment of inertia value of 0.00000557 kgm^2. Then, using the given angular velocity (19.6 rad/s) and the time taken to reach that velocity (0.768 s), you can calculate the angular acceleration (25.52 rad/s^2). Plugging these values into the formula Net torque = Ia, you will get a net torque of 0.142 Nm.

In summary, the correct net torque acting on the CD is 0.142 Nm, not 1827.33 J. It is important to use the correct units and values in calculations to get accurate results.