Find angular velocity from constant linear velocity

In summary, to find the angular velocity in rpm of a rotating disk with a diameter of 2.50m connected to a counter weight through a massless rope, where the rope does not slip and there is no friction on the rim, the circumference of the wheel (PI*diameter) should be divided by the speed of the elevator (25 m/s) to get the period in seconds. The angular frequency can then be found by taking the reciprocal of the period, but to get the answer in rpm, the period should be converted into minutes by dividing by 60. This will give the required revolutions per minute to raise/lower the elevator at 25 m/s.
  • #1
dentulousfing
4
0

Homework Statement



A rotating disk of 2.50m in diameter serves tu connect a counter weight to a mass through a massless rope. The rope does not slip on the disk so, there is no friction on the rim. What angular velocity in rpm must the disk turn to raise the elevator at 25.0 m/s?

Homework Equations


v=r*omega
a(rad)=omega^2*r


The Attempt at a Solution


I am confused here.
since the linear velocity of the rope is constant, its linear acceleration should be zero, and every point on the rope should have the same velocity. Becasue the radius of the rim is constant, the angular velocity should be zero and angular acceleration as well.
a(tan)=r*alpha
alpha=0
a(tan)=0
because the tangential acceleration is zero, then the acceleration vector should have a radial component only: a(rad)=omega^2*r
I could factor out omega from the equation and obtain:
omega=square root of a(rad)/r.. but I don't have the radial component of the acceleration...
should I just use the equation v=omega*r, and factor out omega from it?

Just wondering, if I were given the tension on the rope, caused by the weight of the mass connected to it, or a given displacement with this constant pulling force by the rope on the mass, would these factors just be ignored by the fact that the bofy is moving with a constant velocity, thus, a=0, and the net force on the object is zero as well?
please help
thanks
 
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  • #2
I believe that you should find the circumference of the wheel [ PI * diameter ].
Divide the circumference by the speed the lift is expected to travel (25 m/s); this will give you the period (time for one full rotation of the wheel) in seconds.

Work out the angular frequency by finding the reciprocal of the period [ 1 / period ], but to get your answer in RPM convert the period into minutes rather than seconds by dividing it by 60.

This should give you the answer expected in the question; the required revolutions per minute to raise/lower the lift at 25 m/s.

Please do correct me if I'm wrong, anyone.
 
  • #3




To find the angular velocity from a constant linear velocity, we can use the equation v=r*omega, where v is the linear velocity, r is the radius of the rotating disk, and omega is the angular velocity. In this problem, we are given the linear velocity of the elevator, v=25.0 m/s, and the radius of the disk, r=1.25 m (since the diameter is 2.50m). Substituting these values into the equation, we can solve for the angular velocity:
omega = v/r = 25.0 m/s / 1.25 m = 20 rad/s.

To convert this to rpm, we can use the conversion factor 1 rpm = 2π rad/s, so the angular velocity in rpm would be 20 rad/s * (1 rpm / 2π rad/s) = 3.18 rpm.

As for the confusion about the acceleration and net force, you are correct that since the elevator is moving with a constant velocity, the acceleration and net force on the object would be zero. This means that the tension in the rope would also be zero, since there is no net force acting on the object. However, in this problem, we are not given the tension or displacement of the rope, so we can simply focus on finding the angular velocity from the given linear velocity.
 

1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point, such as an axis or center of rotation. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related by the equation ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the radius of rotation. This means that as the distance from the axis of rotation increases, the angular velocity decreases.

3. Can angular velocity be constant while linear velocity changes?

Yes, it is possible for angular velocity to remain constant while linear velocity changes. This can occur when an object is moving in a circular path at a constant speed, as the linear velocity will change as the distance from the axis of rotation changes, but the angular velocity will remain the same.

4. How do you calculate angular velocity from constant linear velocity?

To calculate angular velocity from constant linear velocity, you can use the equation ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the radius of rotation. Simply plug in the known values and solve for ω.

5. Can angular velocity be negative?

Yes, angular velocity can be negative. A negative angular velocity indicates that the object is rotating in the opposite direction of a positive angular velocity. For example, if a wheel is rotating counterclockwise, it would have a positive angular velocity, but if it were rotating clockwise, it would have a negative angular velocity.

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