Rotational Inertia and Angular Momentum

If you did, then you must've used the fact that the rate of change of angular momentum equals the applied torque, and that angular momentum is equal to rotational inertia times angular velocity. Great job!
  • #1
ScreamingIntoTheVoid

Homework Statement


A disk with a rotational inertia of 8.38 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.03 + 1.01t) N · m. At time t = 1.00 s, its angular momentum is 6.57 kg·m2/s. What is its angular momentum at t = 3.00 s?

Homework Equations


dL/dt= T L=Iw

The Attempt at a Solution


dL/dt=T (my symbol for touque) -> L=5.03t+1.01t^2+C --> 5.03 (1)+ 1.01(1)^2+C= 6.57 -->C=0.53

L=5.03(3)+ 1.01(3)^2 +0.53 --> 24.71 kg*m/s^2

Apparently that's wrong... Help?
 
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  • #2
For the sake of any suffering physics student that comes upon this, remember as I did not the integral of x= (x^2)/2 and you should be able to solve this.
 
  • #3
So, you solved this problem, right?
 

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to change in its rotational motion. It depends on the object's mass, shape, and distribution of mass.

2. How does rotational inertia differ from linear inertia?

Rotational inertia is similar to linear inertia, but instead of an object's resistance to linear motion, it measures its resistance to rotational motion. In other words, it is the rotational equivalent of mass in linear motion.

3. What factors affect rotational inertia?

The main factors that affect rotational inertia are the mass of the object, the radius of rotation, and the distribution of mass. Objects with a larger mass, a larger radius of rotation, and a more spread out distribution of mass have a higher rotational inertia.

4. How is angular momentum related to rotational inertia?

Angular momentum is a measure of an object's tendency to continue rotating. It depends on the object's rotational inertia and its angular velocity (how fast it is rotating). An object with a higher rotational inertia will have a higher angular momentum, and vice versa.

5. How is rotational inertia measured?

Rotational inertia is usually measured experimentally by calculating the moment of inertia for a given object. This involves measuring the object's mass, its distribution of mass, and its radius of rotation, and using these values in the moment of inertia equation. It can also be calculated using calculus for more complex objects.

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