Finding angular speed/accel from tangential speed

In summary, professional recording studios use reel-to-reel tape decks with a constant linear speed of 0.381 m/s. To find the angular speed of the take-up reel, the radius (r) is needed but not given, making the question unsolvable.
  • #1
thatgirlyouknow
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Homework Statement



Professional recording studios often use reel-to-reel tape decks. On such a tape deck, the tape is pulled past the playback head at a constant linear speed of 0.381 m/s. (a) Using the data in part a of the figure, find the angular speed of the take-up reel. (b) After 2.79 x 10^3 s, the take-up reel is almost full, as part b of the drawing indicates. Find the average angular acceleration of the reel with the appropriate sign, where a positive value means the reel is speeding up.


Homework Equations



Vtangential = r*omega (which here will be w)
accelerationtangential = r*alpha (here,alp)


The Attempt at a Solution


.381 m/s = r * w rad/s

In the diagram, r isn't given. Is there a way I can find it? It's constantly changing because of the tape's reeling effect, so I'm not sure how that would fit in.
 

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  • #2
thatgirlyouknow said:
In the diagram, r isn't given
making the question unsolvable.
 

1. What is the formula for finding angular speed from tangential speed?

The formula for finding angular speed (ω) from tangential speed (v) is ω = v/r, where r represents the radius of the circular motion. This formula is derived from the basic definition of angular speed, which is the rate at which an object rotates around a fixed point.

2. How do you convert tangential speed to angular speed?

To convert tangential speed to angular speed, divide the tangential speed (v) by the radius (r) of the circular motion. This will give you the angular speed (ω), which is measured in radians per second (rad/s). Alternatively, you can use the formula ω = 2πv/T, where T represents the period of the circular motion.

3. What is the relationship between tangential speed and angular speed?

Tangential speed and angular speed are directly proportional to each other. This means that as the tangential speed increases, the angular speed also increases, and vice versa. This relationship is described by the formula ω = v/r.

4. How do you find angular acceleration from tangential speed?

To find angular acceleration (α) from tangential speed (v), you can use the formula α = v/r^2. This formula is derived from the definition of angular acceleration, which is the rate of change of angular speed with respect to time. The unit of angular acceleration is radians per second squared (rad/s^2).

5. Can angular speed and tangential speed be negative?

Yes, both angular speed and tangential speed can be negative. A negative angular speed indicates that the object is rotating in the opposite direction of the chosen reference direction, while a negative tangential speed indicates that the object is moving in the opposite direction of the tangent to its circular path. However, in most cases, these values are represented as positive numbers for simplicity.

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