0.32 Phy1320: angular momentum -- the mathematics of torque  (Page 8/13)

However, that would not be a true statement.

Houston, we have a problem

Assume that you do the following to our hypothetical frictionless turntable while it is spinning. Using one finger from each hand, press on opposite sidesof the turntable, applying an equal force directed towards the center of the turntable on each side of the turntable.

No net force

In this case, the turntable would not experience any net forces. Assuming that you are facing north when you do this,and that you press on the east and west sides of the turntable, the frictional forces generated by your fingers would be directed in opposite directions.

If the turntable were spinning counter clockwise (when viewed from the top), thefrictional force created by your finger on the east side would be directed toward the south. The frictional force created by your finger on the west sideof the turntable would be directed toward the north.

From a translational viewpoint, at least, there would be no net force applied to the turntable. The force that points to the north would be cancelledby the force that points to the south. The force that points to the east would be cancelled by the force that points to the west. Therefore, the turntablewould be in translational equilibrium.

Acceleration would no longer be zero

Despite that, the velocity would be decreased meaning that the acceleration would no longer be zero. From this we might conclude thatjust because a rotating object is in translational equilibrium, it is not necessarily in rotational equilibrium.

The world of torque

We have just entered the world of torque with this hypothetical experiment. Torque is a quantity that plays a role in rotation that is analogous to the role that force plays in translation.

However, torque is not separate from force. It is not possible to exert a torque without exerting aforce.

Torque is a measure...

In anecdotal terms, torque is a measure of how effective a force is at changing the angular velocity of an object. Stated differently, torque is ameasure of how effective a force is at causing an object to have a non-zero angular acceleration.

Angular acceleration can be either positive or negative

For an object that is rotating about a fixed axis (or is capable of rotating about a fixed axis), such as my turntable,torque can either increase or decrease the angular velocity of the object.

Net translational force was zero

When you pressed your fingers on my turntable as described earlier, the net translational force applied to the turntable was zero. Therefore, the turntable remained intranslational equilibrium, meaning that it didn't go sliding towards the edge of the table.

Net torque was not zero

However, the net torque was not zero, so it was not in angular equilibrium. The kinetic frictional forces generated on each side of theturntable resulted in the same algebraic sign of non-zero angular acceleration.

Each force caused the angular velocity to decrease. The two torques created by the kinetic friction forces were not only equal, they had the same algebraic sign.Therefore, the turntable experienced a non-zero net torque.