# Is there a true upward force on a rotating object?

• Surya97
In summary, the torque on a rotating object is the resultant of the force vector and the lever arm position vector. However, there is no actual acceleration felt by the object upward along the axis in the direction of the torque vector. This is because the cross product is needed to multiply the vectors, and as such, the actual direction of the cross product vector does not accurately reflect the actual direction of the torque.
Surya97
I understand that the torque on a gyrating object is defined as the force vector cross multiplied by the lever arm position vector, which produces a resultant vector that is normal to both of the original vectors. However, when an object (let's say a disk) is rotating about an axis counterclockwise, there is no actual acceleration felt by the object upward along the axis in the direction of the torque vector. Is this because cross multiplication is needed to multiply the two vectors and get a vector, and as such, the actual direction of the cross product vector does not accurately reflect the actual direction of the torque?

It reflects the direction of the torque, not the force, and the direction of the net torque when greater than 0 is in the direction of the angular acceleration, perpendiculTto the force and position vectors. The direction represents the axis of rotation. It s often convenient to indicate the direction as clockwise or counterclockwise , but when addng torques about different axes, the resultant torque is found by summing the individual torque vectors vectorialy.

You didn't answer my question. I was asking why the object didn't experience movement in the direction of the torque vector (which is along the axis due to it being a cross product between the force and lever arm). Is the torque vector only pointing upward because of the mathematical convenience of using a cross product?

To clarify the question,

What does the torque vector itself tell you? What happens in the direction that the torque vector is pointing in (upward along the axis)? Is there an acceleration in the direction of the torque?

Surya97 said:
I was asking why the object didn't experience movement in the direction of the torque vector

Because it's the torque, not the force.

What does the torque do in that direction?

Torque is defined as the "tendency" for a force to cause the object to turn at a certain distance from the center of gravity. However, why does this tendency manifest itself as an upward vector?

How do you use the torque vector itself?

Is there an intuitive reason for the torque vector's direction?

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Since the torque vector is normal to both vectors, you can find the plane of rotation with the torque vector function coefficients.

Based on the direction of the vector, you can find the direction of rotation.

The magnitude of the torque tells you the "amount" of rotation.

However, this means that the vector itself isn't mathematically useful.

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It is mathematically useful, because you can add torque vectors together to get the net torque, in the same way that you can add force vectors together to get the net force. Where you seem to be getting hung up is that there's no actual motion in the direction of this vector. That's because the vector isn't meant to signify a direction of motion; it signifies the axis of rotation and the magnitude of the angular quantity under consideration. That is perhaps a bit more abstract than force vectors (at least in terms of visualizing them), but they seem just as mathematically useful to me.

Surya97 and PhanthomJay
Thanks.

## 1. What is the Coriolis effect and how does it relate to the upward force on a rotating object?

The Coriolis effect is a phenomenon that occurs when an object is moving in a rotating reference frame. It causes the object to appear to deviate from its straight path due to the rotation of the frame. In the case of a rotating object, the Coriolis effect is responsible for the upward force that is felt. This force acts in the opposite direction of the rotation and is perpendicular to the object's velocity.

## 2. How does the direction and speed of rotation affect the upward force on a rotating object?

The direction and speed of rotation play a crucial role in determining the magnitude of the upward force on a rotating object. The higher the speed of rotation, the greater the force will be. Additionally, the direction of rotation also affects the direction of the force. For example, an object rotating counterclockwise will experience an upward force in the direction of the rotation, while an object rotating clockwise will experience an upward force in the opposite direction.

## 3. Is the upward force on a rotating object the same as the centrifugal force?

No, the upward force on a rotating object is not the same as the centrifugal force. The centrifugal force is an outward force that acts on an object in a rotating frame of reference, while the upward force is an inward force that acts on the object. These two forces are equal in magnitude but act in opposite directions and have different effects on the rotating object.

## 4. How does the radius of rotation affect the upward force on a rotating object?

The radius of rotation is directly related to the upward force on a rotating object. As the radius increases, the distance between the object and the axis of rotation also increases. This results in a larger lever arm, which in turn increases the upward force on the object. This can be observed in everyday objects such as a spinning top, where the upward force increases as the top's radius of rotation increases.

## 5. Is there any other force acting on a rotating object besides the upward force?

Yes, there are other forces that can act on a rotating object besides the upward force. These include the Coriolis force, which was mentioned earlier, and the centripetal force. The centripetal force acts in the direction of the object's motion and keeps it moving in a circular path. In a rotating reference frame, the centripetal force is provided by the upward force. Additionally, there may also be other external forces acting on the object, such as friction or air resistance, that can affect its rotation.

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