Calculate Rotational Velocity of Object Around Fixed Point

In summary, the velocity of an object rotated around a fixed point, such as a hand on a clock, can be calculated by dividing the rotational velocity by the radius of the object. This rotational velocity is expressed in frequency, measured in units of 1/s or radians per second, and is the same for all points on the object, regardless of their distance from the center.
  • #1
einsteinian77
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How could i calculate the velocity of an object rotated around a fixed point such as a hand on a clock. It seems as though each section of the hand would have a different velocity, the end part being the fastest while the beginning part being the slowest if not moving at all. I am guessing the velocity would be expressed in frequency somehow.
 
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  • #2
Originally posted by einsteinian77
Im guessing the velocity would be expressed in frequency somehow.

That's correct, einsteinian77. Since the rotational velocity v increases proportional with radius r (distance from center), you define the angular velocity
[nu] = v/r.
This is the same for all points. The unit is 1/s. You could also say it's radians per second, since by integrating you get the angle:
[alpha] = a/r
where a is the arc length, and [alpha] is measured in radians.
 
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1. How do you calculate the rotational velocity of an object around a fixed point?

To calculate the rotational velocity of an object around a fixed point, you need to know the distance from the object to the fixed point, as well as the angle and time it takes for the object to complete one full rotation. You can then use the formula: rotational velocity = (2π * distance) / (time * cos(angle)).

2. What is the unit of measurement for rotational velocity?

The unit of measurement for rotational velocity is radians per second (rad/s). This measures the angular speed of the object as it rotates around the fixed point.

3. Can the rotational velocity of an object around a fixed point change?

Yes, the rotational velocity of an object around a fixed point can change if the distance from the object to the fixed point changes, or if the time or angle of rotation changes. It can also change if an external force, such as friction or gravity, acts on the object.

4. How is rotational velocity related to angular velocity?

Rotational velocity and angular velocity are closely related, as they both measure the rate of rotation of an object. Rotational velocity specifically measures the linear speed of an object as it rotates around a fixed point, while angular velocity measures the angle of rotation per unit of time. They are mathematically related by the formula: rotational velocity = angular velocity * distance.

5. How is the rotational velocity of a point on the edge of a rotating object different from the rotational velocity at the center of the object?

The rotational velocity at the edge of a rotating object is greater than the rotational velocity at the center of the object. This is because the point at the edge travels a greater distance in the same amount of time compared to a point at the center, resulting in a higher linear speed and rotational velocity.

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