Easy angular velocity question

In summary, a solid disk with a radius of 1.4cm has 2.0m of string wound on to its circumference. The string is pulled off the disk by a constant force in a time of 7.3s. The final angular velocity of the disk is 39.1 rad/s, calculated by using the equation ω = v/r and solving for v, which gives a value of 0.274 m/s. The incorrect answer of 19.6 rad/s was obtained by dividing the velocity by the radius without considering the time it takes to pull off the string. The correct answer takes into account the constant force and time, resulting in a final angular velocity that is twice the incorrect answer.
  • #1
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Homework Statement



A solid disk with a radius of 1.4cm is a rest. The disk has 2.0m of string wound on to its circumference. The string is pulled off the disk by a constant force in a time of 7.3s. What is the final angular velocity of this disk?


Homework Equations



v = r*ω

The Attempt at a Solution



The correct answer is 39.1 rad/s but I keep getting half of that (19.6 rad/sec).

Since ω = v/r, I solve for v:

2m/7.3 sec = 0.274 m/s

then ω = (0.274 m/s)/(0.014 m) = 19.6.

what am I doing wrong? the correct answer is 39.1
 
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  • #2
Does a constant force mean you have constant velocity or acceleration?
 

Related to Easy angular velocity question

1. What is angular velocity?

Angular velocity is the measure of how fast an object is rotating around a fixed point or axis. It is usually measured in radians per second.

2. How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in angle (in radians) by the time it takes for that change to occur. It is represented by the symbol ω and the formula is ω = Δθ / Δt.

3. What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of rotational speed, while linear velocity is a measure of straight-line speed. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

4. How is angular velocity used in real life?

Angular velocity is used in many real-life applications, such as measuring the speed of a spinning object, calculating the rate of rotation in machines, and determining the speed of planets and other celestial bodies in their orbits. It is also used in sports, such as measuring the speed of a pitched baseball or the rotation of a figure skater.

5. How does angular velocity relate to centripetal force?

Angular velocity and centripetal force are related through the formula F = mω²r, where F is the centripetal force, m is the mass of the object, ω is the angular velocity, and r is the radius of the circular motion. This formula shows that as the angular velocity increases, the centripetal force required to keep the object in its circular path also increases.

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