Final answer:
This physics problem involves calculating a particle's angular momentum, torque, and the rate of change of angular momentum about the origin, using the principles of rotational dynamics and vector cross product formulas.
Step-by-step explanation:
The problem given involves a particle with mass, position, velocity, and force acting upon it, and we're asked to calculate angular momentum, torque, and the rate of change of angular momentum. This is a classical mechanics problem in physics that requires knowledge of the respective formulas and an understanding of vector cross products.
(a) Angular Momentum
Angular momentum L of a particle about a point is given by the cross product of the position vector r and the linear momentum p of the particle, which is mass times velocity (L = r x p). Using the given position (x = 7.86 m, y = 9.84 m) and mass (9.29 kg) with the unspecified velocity, we would apply the formula to find the angular momentum about the origin.
(b) Torque
Torque \(\tau\) is calculated as the cross product of the position vector and the force vector (\(\tau = r x F\)). Since the only force given is in the negative x direction, we use this along with the position of the particle to calculate torque about the origin.
(c) Rate of Change of Angular Momentum
The rate of change of angular momentum is equal to the net external torque acting on the particle. By calculating the torque as found in (b), we will know the rate of change of angular momentum, assuming that the force remains constant and is the only force acting on the particle.