A particle is acted on by two torques about the origin: T1 has a magnitude of 4.3 N*m and is directed in the positive direction of the x axis, and T2 has a magnitude of 3.2 N*m and is directed in the negative direction of the y axis. What are the magnitude [in N*m] and direction [counterclockwise from the +x axis] of dL/dt, where L is the angular momentum of the particle about the origin?
.. is there an equation that finds the magnitude of the net torques? help?
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* Physics - Torque - bobpursley, Saturday, March 31, 2007 at 8:46am
Add the torques as vectors.
T=I * angular acceleration is a VECTOR equation, as is
angularmomentum=I * angularvelocity
angular veloicty= wo + angacceleration*time
is also a vector equation. So add the vectors for T, solve for angacceleration, then solve for angular momentum.
Now on directions. When one indicates direction on a circular torque, or velocity, as in this case , use the right hand rule. Your stating the T1 is in the direction of x means it is rotating in the YZ plane, from Y to Z. I hope this is what you meant in the problem description.
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So for Torque the net Torque is:
Tnet = (4.3 N*m)i - (3.2 N*m)j
T = I*angular acceleration
How do I calculate Inertia if I am not given a mass of the particle?
Actually you cant. You need to know the mass of the particle, AND its location in relation to the origin. THe statement did not mention either.
I have read the problem several times, and I can surmise what it meant on that mass, or location. Perhaps it meant a point charge M, at the origin, but perhaps again not.
I agree, it has me baffled.
To find the magnitude and direction of the net torque acting on the particle, you need to add the individual torques as vectors.
In this case, we have T1 = 4.3 N*m in the positive x-axis direction and T2 = 3.2 N*m in the negative y-axis direction.
To add these torques as vectors, you can use the vector addition method. Simply add the components of the torques in each direction separately.
T_net_x = T1_x + T2_x = 4.3 N*m + 0 N*m = 4.3 N*m
T_net_y = T1_y + T2_y = 0 N*m + (-3.2 N*m) = -3.2 N*m
So the net torque acting on the particle is T_net = (4.3 N*m)i - (3.2 N*m)j.
Now, to find dL/dt (the rate of change of angular momentum), we can use the equation dL/dt = T_net. Since angular momentum is defined as L = I * angular velocity, where I is the moment of inertia and angular velocity is the rate of change of angular displacement, we can rewrite the equation as dL/dt = I * angular acceleration.
However, we are not given the mass or the moment of inertia of the particle. Without this information, we cannot calculate the magnitude and direction of dL/dt. The problem statement is not clear in providing the necessary information.
In conclusion, we are unable to answer the question without knowing the mass or the moment of inertia of the particle.