The position vector of a particle of mass m = 2kg in the xy plane is given: r = (t-2)i + (2t +1)j (meter) where t is in seconds . Find the torque exerted on the particle about the origin.
To find the torque exerted on the particle about the origin, we need to compute the cross product of the position vector with the force vector.
Torque (τ) is defined as the cross product of the position vector (r) and the force vector (F):
τ = r x F
Since we are only given the position vector (r), we need to determine the force vector first. In this case, the problem statement does not provide any force information, so we need to make some assumptions.
Let's assume that the force acting on the particle is perpendicular to the xy-plane, and its magnitude is constant. Therefore, the force vector can be represented as F = Fk, where F is a constant scalar.
Now, we can calculate the torque by taking the cross product of the position vector (r) and the force vector (F):
τ = r x F
= (t - 2)i + (2t + 1)j x Fk
= [(2t + 1)F]i - [(t - 2)F]j
Since torque is a vector quantity, the result is a vector with i and j components. The torque acting on the particle about the origin is given by:
τ = [(2t + 1)F]i - [(t - 2)F]j
Please note that without the force information, we cannot determine the exact torque value but we can express it in terms of t and F.