A force of 100 N is applied straight down to lower a handle from 45˚ above the horizontal to 45˚ below it. The handle is 1 m long and the force is applied at its end throughout the motion. What is the rate of change of the moment as the angle of the handle moves? What if the force moved down in a straight line, rather than remaining at the end of the handle?

To calculate the rate of change of the moment, we need to find the change in moment and divide it by the change in angle.

First, let's determine the moment at different angles. The moment (torque) is calculated as the force multiplied by the perpendicular distance from the pivot point (fulcrum or axis of rotation).

In this case, we have a handle that is 1 meter long, and the force is applied at its end throughout the motion. So the perpendicular distance remains constant at 1 meter.

Now, let's find the moment at 45˚ above the horizontal and 45˚ below it.

1. Moment at 45˚ above the horizontal:
Moment = Force × Perpendicular distance
= 100 N × 1 m
= 100 Nm

2. Moment at 45˚ below the horizontal:
Moment = Force × Perpendicular distance
= 100 N × 1 m
= 100 Nm

Since the perpendicular distance remains the same throughout the motion, the moment does not change with the angle. So the rate of change of the moment is zero.

Now, let's consider what happens if the force moves down in a straight line, rather than remaining at the end of the handle.

In this case, the perpendicular distance between the force and the pivot point will change as the force moves down. The moment will be different at different angles.

To calculate the rate of change of the moment, we need to determine the moment at different angles before proceeding with the calculations. Unfortunately, the angle at each instance hasn't been provided in the question. Could you please provide the specific angles at which you would like to calculate the rate of change of the moment?