Question

At time t,  r→ = 1.70t² î - (7.60t + 7.80t²) ĵ gives the position of a 3.0 kg particle relative to the origin of an xycoordinate system ( r→ is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 6.50 s (b) Is the magnitude of the particle’s angular momentum relative to the origin increasing, decreasing, or unchanging?

Answer 1

The given position vector is
   
So, the velocity
   
And the acceleration of the particle is
  
And so, the force on the particle is
  
  

a)

   And so, the torque on the particle is
  
   
   
  
  
Now at time t = 6.5 s, we have the torque
     
     

b)
The angular momentum is
     
  
   
  
   
So, the magnitude of the angular momentum is
   
As the magnitude varies as the t^2, so, the magnitude of the angular momentum increases with time t.