Answer:
Angular momentum, [tex]L=6.47\times 10^{-3}\ m[/tex]
Explanation:
It is given that,
Radius of the axle, [tex]r=3.21\ mm=3.21\times 10^{-3}\ m[/tex]
Tension acting on the top, T = 3.15 N
Time taken by the string to unwind, t = 0.32 s
We know that the rate of change of angular momentum is equal to the torque acting on the torque. The relation is given by :
[tex]\tau=\dfrac{dL}{dt}[/tex]
Torque acting on the top is given by :
[tex]\tau=F\times r[/tex]
Here, F is the tension acting on it. Torque acting on the top is given by :
[tex]\tau=2F\times r[/tex]
[tex]2T\times r=\dfrac{L}{t}[/tex]
[tex]L=2T\times r \times t[/tex]
[tex]L=2\times 3.15\times 3.21\times 10^{-3}\times 0.32[/tex]
[tex]L=6.47\times 10^{-3}\ m[/tex]
So, the angular momentum acquired by the top is [tex]6.47\times 10^{-3}\ m[/tex]. Hence, this is the required solution.
