At time t, gives the position of a 3.0 kg particle relative to the origin of an xy coordinate system ( ModifyingAbove r With right-arrow is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 7.46 s (b) Is the magnitude of the particle’s angular momentum relative to the origin increasing, decreasing, or unchanging?

Complete Question

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a

The torque acting on the particle is  

b

The magnitude of the angular momentum increases relative to the origin

Explanation:

From the equation we are told that

      The position of the particle is  

       The mass of the particle is

        The time is  t

The torque acting on  the particle is mathematically represented as

where is change in angular momentum which is mathematically represented as

Where X mean cross- product

    is the velocity which is mathematically represented as

Substituting for  

Now the cross product of is  mathematically evaluated as    

So the angular momentum becomes

Substituting for m

Substituting into equation for torque

The magnitude of the angular momentum can be evaluated mathematically as

From the is equation we see that the magnitude of the angular momentum is varies directly with square of the time so it would relative to the origin because at the origin t= 0s and we move out from origin t increases hence angular momentum increases also

b would be the answer