A dumbbell consists of two equal compact masses of 2 kg each, connected by a massless rod of length 0.8 metres.

What is the moment of inertia of the dumbbell about an axis through the centre of, but perpendicular to, the rod?

could someone just tell me how to get started on this as i'm completely lost and ive an exam in three weeks:(

add up the m r^2

the center of mass is in the middle.
Therefore r for each = 0.4 meters
For each of them m r^2 = 2*.4*.4 = 0.32
So the total I = 0.64

thats great thanks very much

(ii) Using the parallel-axis theorem or otherwise, find the moment of inertia of the dumbbell about an axis through one of the masses but perpendicular to the rod

and for this question i need :
I = Ic.m. + Md2
thats right isnt it?

Yes, M is the total mass and d is .4 meters

(iv) A tangential force of 20N is applied to one of the masses in the plane of rotation of (iii) above for 3.0 s . (Both the instantaneous velocity of the mass and the applied force are pointing in the same direction at all times). What is the final angular velocity of the rod?

for this will i need to use te formula for torque?
i can get very little information from this question any help you could give qould be great

Sure! I can help you get started with finding the moment of inertia of the dumbbell.

To find the moment of inertia, you need to consider the individual masses and their respective distances from the axis of rotation. In this case, the axis of rotation is through the center of the dumbbell and perpendicular to the rod.

Here's how you can proceed:

1. Divide the dumbbell into two equal masses of 2 kg each. These two masses are compact and located at the ends of the rod. Let's call each of these masses "m".

2. The length of the rod is given as 0.8 meters. So, the distance from the axis of rotation to each of the masses is half of this length, which is 0.4 meters. Let's call this distance "r".

3. The formula for the moment of inertia of a point mass rotating about an axis is given by I = m * r^2, where "m" is the mass and "r" is the distance from the axis. Since we have two equal masses, we can calculate the moment of inertia for each mass separately and then add them together.

4. The moment of inertia for each mass is I = m * r^2. Plugging in the values, we get I = 2 kg * (0.4 m)^2.

5. Calculate the moment of inertia for each mass separately, and then add them together. So the total moment of inertia of the dumbbell is:

I_total = I_mass1 + I_mass2 = 2 kg * (0.4 m)^2 + 2 kg * (0.4 m)^2.

6. Simplify the equation by performing the calculations. You will get the moment of inertia of the dumbbell about the given axis.

I hope this helps you get started on finding the moment of inertia of the dumbbell! Remember to review the formulas and units to ensure accurate calculations. Good luck with your exam!