We can cause this rectangle to rotate by applying a force at this location.
If we apply a force at this other location,
then the rectangle will rotate in the opposite direction.
If we apply a force here at the axis of rotation,
the rectangle won’t rotate in either direction,
since it does not know in which direction to turn.
The further away from the center a force is from the axis of rotation,
the more the force will cause the rectangle to turn.
The same thing is true for all objects.
If we apply two forces of equal strength
causing the rectangle to rotate in opposite directions,
then the force that is further away from the axis of rotation will win out.
In order for the two forces to balance,
the force which is closer to the axis of rotation needs to be of a greater strength.
But, if the weaker force moves even further away from the axis of rotation,
it will win out again.
This is why a lever allows us to lift objects that would
otherwise be far too heavy to lift with our bare hands.
If we are allowed to change where our axis of rotation is located, then
the point at which the effects of all the gravitational forces would cancel out,
and cause no net rotation, is what we call the object’s center of mass.
If an object is in space with no fixed axis of rotation,
then the object will rotate around its center of mass.
The center of mass does not necessarily have to be a point on the object.
The total motion of an object through space
is the path followed by its center of mass,
plus the rotation of the object around the center of mass.
A force on the object can simultaneously change both the path of the center of mass,
and the object’s rotation around its center of mass.
The path of the center of mass is affected by the sum of all the forces on an object,
regardless of where on the object the force is applied.
Where on the object the force is applied is important
only with regards to how it will change the object’s rotation.
All the forces on the object affect the center of mass’s path through space.
But, not all the forces will affect an object’s rotation.
The forces that are applied to an object can be represented as an arrow,
with the strength of the force represented by the length of the arrow.
This arrow can be thought of as the combination
of smaller arrows which are 90 degrees to each other.
This smaller arrow is the only portion of this force
that contributes to changing the rotation of the object.
Therefore, the how much a force affects the rotation of an object
depends on the direction of the force,
in addition to the force’s strength,
and where the force is located.
The total amount by which a force affects the rotation of an object
is a combination of all these three factors, and we refer to this as the torque.
The torque can be represented by an arrow.
The direction of the arrow indicates
the axis around which the torque is trying to rotate the object.
The length of the arrow indicates the strength of the torque.
If there are multiple forces acting to cause an object to rotate,
then the torques produced by these forces add together.
In addition to the strength and direction of the torque, there is one other
factor that determines how much the rotation of an object is affected.
This is how much mass is present, and how the mass is distributed throughout the object.
Just as it is harder to lift an object on a lever if it has more mass
Or if the mass is further away from the axis of rotation,
It is similarly harder to change the rotation of an object if it has more mass,
Or if the mass is further away from the axis of rotation.
If an object has more mass, or if the mass of the object is further away
from the axis of rotation, we give this a name, and we say that
the object has a higher “moment of inertia.”
The rate at which an object’s rotation changes is
the strength of the torque divided by the object’s moment of inertia.
The rate at which an object’s rotation changes
is what we call the angular acceleration.
In the case of linear motion through space, the linear acceleration of an object is
the strength of the force divided by the mass.
The equation for angular acceleration is very similar to this.
Acceleration is replaced with angular acceleration.
Force is replaced with torque.
And mass is replaced with moment of inertia.
The angular acceleration is the torque divided by the moment of inertia.
In the case of linear motion,
the speed and direction of an object is what we refer to as velocity.
In the case of rotation,
the speed and direction of rotation is what we refer to as angular velocity.
In the case of linear motion, an object’s mass multiplied by its velocity
is what we refer to as the object’s momentum.
In the case of rotation, we have a similar equation.
Velocity is replaced with angular velocity.
As before, mass is replaced with moment of inertia.
And momentum is replaced with a new term, called angular momentum.
Changing how far away a mass is from the axis of rotation
changes the object’s moment of inertia
and it changes the object’s angular velocity.
But, since the angular momentum is
the angular velocity multiplied by the moment of inertia,
the angular momentum stays constant.
In the absence of an external torque,
the angular momentum of an object is always constant.
This is the same way that in the absence of an external force,
the momentum of an object always stays constant.
Since there are no external forces and no external torques
acting on the entire Universe as a whole,
this means that both the momentum and the angular momentum
of the entire Universe as a whole is always constant.
Much more information about the laws of motion
is available in the other videos on this channel,
and more videos will be coming soon.