Some questions about calculateJacobian()

[zoukj]

Input

1. objPosition: This variable don't include the base position and orientation. So the Jacobian can only be used to compute velocity relative to the base, right?
2. objVelocities: I thought Jacobian is a function of joint position. Why we need velocity to compute Jacobian?
3. objAcceleration: What's the use of desired joint accelerations for Jacobian?

Example

If I use Jacobian to compute angular velocity of a link, it will be equal to the result of getLinkState().
(for a rigid body, angular velocity should be equal everywhere on it)
but I found they are not the same, what's wrong with my code?

import time
    # TODO: for example, about the last link and joint
    index = p.getNumJoints(model_id)-1
    while True:
        base_lin_vel, base_ang_vel = np.array(p.getBaseVelocity(model_id))
        positions, velosities = [], []
        for i in range(p.getNumJoints(model_id)):
            pos, vel = p.getJointState(model_id, i)[0:2]
            positions.append(pos)
            velosities.append(vel)
            pass
        q_dot = np.concatenate([base_ang_vel,
                                base_lin_vel,
                                velosities])
        lin_J, ang_J = p.calculateJacobian(model_id,
                                           linkIndex=index,
                                           localPosition=[0, 0, 0],
                                           objPositions=positions,
                                           objVelocities=velosities,
                                           objAccelerations=len(positions)*[0.])
        lin_J, ang_J = np.array(lin_J), np.array(ang_J)
        base_orn = p.getBasePositionAndOrientation(model_id)[1]
        # only consider the angular velocity
        vel = ang_J @ q_dot
        vel = p.rotateVector(base_orn, vel)
        print(vel)
        actual = p.getLinkState(model_id, index,
                                computeLinkVelocity=1,
                                computeForwardKinematics=1)[7]
        print(actual)
        print('~'*50)
        p.stepSimulation()
        time.sleep(1./240)
        pass