Why the components of position vectors along axis are not needed for determining the torque in the rigid body?

Explain the torque acting on a rigid body.

A particle moving parallel to x-axis as shown in fig. such that at all instant the y-axis component of its position vector is constant and is equal to 'b'. Find the angular velocity of the particle about the origin when its radius vector makes angle theta from the axis.

Explain with defination of angular position, angular displacement and angular speed for the motion of rigid body.

Which component of torque is responsible for the rotation motion about Z-axis?

hatiandhatj are unit vectors along x - and y- axis respectively . What is the magnitude and direction of the vectors hati+hatjandhati-hatj ? What are the components of a vector A=2hati+3hatj along the directions of hati+hatjand hati-hatj ? [ You may use graphical method]

If vecF is the force acting on a particle having position vector vecr and vectau be the torque of this force about the region, then :

A particle is moving along a straight line parallel to x-axis with constant velocity and position vector is vthati+bhatj . Find angular momentum about the origin in vector form :

A disc is rotating with angular velocity omega . A force F acts at a point whose position vector with respect to the axis of rotation is r. The power associated with torque due to the force is given by

The x and y-components of vector A are 4 m and 6 m respectively. The x and y-components of vector A + B are 10 m and 9 m respectively. Calculate for the vector B the following: (a) its x and y-components (b) its length (c ) the angle it makes with x-axis.

The motion of a particle is defined by the position vector vec(r)=(cost)hat(i)+(sin t)hat(j) Where t is expressed in seconds. Determine the value of t for which positions vectors and velocity vector are perpendicular.