Why is there angular acceleration in a non-spinning gyroscope?

In summary, the author derives that the angular acceleration is g/r which is non zero. This is due to the disc being constrained to move in a circle by the force at the hinge and the radial acceleration is perpendicular to the circle.
  • #1
JC2000
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I was watching the above video which is part of a series explaining the mechanics behind a gyroscope. In the video the author explains the mechanics of the gyroscope when stationary (the disc is not rotating). Here he derives a result that the angular acceleration is g/r which is non zero.

1.Does the angular acceleration refer to the rotation of the disc and the rod about the hinge (due to the torque)?
2.If so, how is the relationship between the angular acceleration and tangential acceleration derived?
3. Is the tangential acceleration tangential to the curve charted by the falling disc?
4. If I understand correctly, the angular acceleration is a function of r, which is the perpendicular distance between the line of action of the force (m*g) and the axis about which rotation occurs. Thus as the disc falls at an angle, r changes, and hence angular acceleration changes (?). If so why is the tangential acceleration equal to acceleration due to gravity only initially?

Thank you for your time!
 
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  • #2
JC2000 said:
Summary:: In the video linked below the gyroscope disc is not rotating. How can it have an angular acceleration in that case?



I was watching the above video which is part of a series explaining the mechanics behind a gyroscope. In the video the author explains the mechanics of the gyroscope when stationary (the disc is not rotating). Here he derives a result that the angular acceleration is g/r which is non zero.

1.Does the angular acceleration refer to the rotation of the disc and the rod about the hinge (due to the torque)?
2.If so, how is the relationship between the angular acceleration and tangential acceleration derived?
3. Is the tangential acceleration tangential to the curve charted by the falling disc?
4. If I understand correctly, the angular acceleration is a function of r, which is the perpendicular distance between the line of action of the force (m*g) and the axis about which rotation occurs. Thus as the disc falls at an angle, r changes, and hence angular acceleration changes (?). If so why is the tangential acceleration equal to acceleration due to gravity only initially?

Thank you for your time!


1) Yes.

2) For circular motion, if the angle is measured in radians, then we have ##a = r\alpha##. This follows from the definition of the radian.

3) The disc is constrained to move in a circle: the tangential acceleration is defined as the component acceleration tangential to the circle; the radial acceleration is defined as the component perpendicular to circle.

4) Initially (only instantaneously) there is negligible force at the hinge. As the disc falls a force at the hinge and along the arm is required to constrain the disc to its circular path: gravity alone would accelerate it vertically. The acceleraion after the first instant is, therefore, due to the sum of these forces.
 
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  • #3
PeroK said:
1) Yes.

2) For circular motion, if the angle is measured in radians, then we have ##a = r\alpha##. This follows from the definition of the radian.

3) The disc is constrained to move in a circle: the tangential acceleration is defined as the component acceleration tangential to the circle; the radial acceleration is defined as the component perpendicular to circle.

4) Initially (only instantaneously) there is negligible force at the hinge. As the disc falls a force at the hinge and along the arm is required to constrain the disc to its circular path: gravity alone would accelerate it vertically. The acceleraion after the first instant is, therefore, due to the sum of these forces.
Thank you for the clear explanation!
 

FAQ: Why is there angular acceleration in a non-spinning gyroscope?

1. Why does a non-spinning gyroscope experience angular acceleration?

A non-spinning gyroscope experiences angular acceleration because of the conservation of angular momentum. When a force is applied to the gyroscope, it causes a torque, which results in a change in the direction of the gyroscope's angular momentum. This change in angular momentum causes the gyroscope to experience angular acceleration.

2. How does angular acceleration affect a non-spinning gyroscope?

Angular acceleration affects a non-spinning gyroscope by causing it to precess, which is the gradual change in the orientation of the gyroscope's spin axis. This precession can be seen as the gyroscope rotating around a fixed point, known as the axis of precession.

3. Can a non-spinning gyroscope have constant angular velocity?

No, a non-spinning gyroscope cannot have constant angular velocity. This is because angular velocity is the rate of change of angular displacement, and in order for there to be a change in angular displacement, there must be angular acceleration. Therefore, a non-spinning gyroscope will always experience some level of angular acceleration.

4. How does friction affect the angular acceleration of a non-spinning gyroscope?

Friction can affect the angular acceleration of a non-spinning gyroscope by creating a torque that opposes the initial force applied to the gyroscope. This can cause the gyroscope to experience a decrease in angular acceleration or even come to a stop, depending on the strength of the frictional force.

5. Can the angular acceleration of a non-spinning gyroscope be controlled?

Yes, the angular acceleration of a non-spinning gyroscope can be controlled by adjusting the magnitude and direction of the initial force applied to the gyroscope. By changing the force, the resulting torque and angular acceleration can also be changed. Additionally, external factors such as friction and air resistance can also be controlled to some extent to affect the angular acceleration of the gyroscope.

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