Question

when a car drives off a cliff it rotates foward as it falls.For a higher speed off a cliff, will it rotate more or less. (consider the time that the unbalanced torque acts.)

Answer 1

It will rotate with a greater angular velocity when it is travelling slowly. Before we go into the whys and hows, here is a little experiment you can try.

Take a coin and put it on a table with a part of it over the edge but the center still on the table. We know from experience the coin won't fall off. Now gently nudge it and you can almost certainly imagine (or see if you actually do it) that the coin will rotate slowly and falls. Next, we hit it of the table, and it'll fly horizontally off the table top like a disc, hardly rotating. A pecnil can be used too if you hit it hard at the eraser end. It'll fly off like a missile.

Now for the explanation.

When the front of the car is just over the edge, the car will not rotate as the center of mass is still above ground and thus negates gravity's torque.

When the center of mass is just over the edge, gravity's torque begins to act though it will be weak. It gets stronger as more and more of the car is over the edge. When the car is completely air borne, it becomes zero.

Torque causes angular acceleration and if the car is moving slowly, it acts for a long time and gives a car a high value of angular velocity (it rotates fast). If it is going fast, torque acts for so little a time, it doesn't give it any considerable angular velocity.


The car is moving slowly for this graph of torque and time. Torque acts for a decent amount and time and the area under the graph is change in angular momentum.


The area is this graph is smaller since torque doesn't act for too long. Hence, final angular momentum is smaller.