Calculating angular speed out of tangential speed

In summary, particle A is moving at a constant tangential speed of 2m/s on a circumference of radius 5m. Particle B, which has an angular speed twice that of particle A, is performing a uniform circular motion on a circumference with a radius of 10m. Using the equation v/r = ω, we can find that the tangential speed of particle B, v2, is 8m/s.
  • #1
catstevens
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Homework Statement



A particle A is moving at constant tangential speed v1 = 2m/s on a circumference of radius r1 = 5m.
Particle B is performing a uniform circular motion on a circumference whose radius is r2 = (2)r1.
Find the tangential speed of v2 of particle B assuming that the angular speed w2 of particle B is twice the angular speed w1 of particle A


Homework Equations


Tangential speed at 10m from the axis point is 2 times the tangential speed at 5m from the axis.


The Attempt at a Solution



v1=2m/s at 5m from the axis of rotation
IF particle B was rotating at the same angular speed...v2=4m/s
BUT w2 = 2w1 SO v2=8m/s
 
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  • #2
That looks correct.

v/r = 2/5 = ω

2ω = 4/5

v = ω *r = 4/5*10 = 8
 
  • #3


I would approach this problem by first understanding the concept of tangential speed and angular speed. Tangential speed is the linear speed of an object moving along a circular path, while angular speed is the rate of change of angular displacement. These two quantities are related by the formula v = rω, where v is tangential speed, r is the radius of the circular path, and ω is the angular speed.

In this problem, we are given the tangential speed of particle A, v1, and the radius of its circular path, r1. We are also told that particle B is rotating at twice the angular speed of particle A, and its circular path has a radius of 2r1. To find the tangential speed of particle B, we can use the formula v = rω and substitute in the given values.

v2 = (2r1)(2w1) = 4r1w1

However, we are given the tangential speed at 5m from the axis for particle A, not at the axis point itself. To account for this, we can use the given information that the tangential speed at 10m from the axis is twice that at 5m. This means that v1 at 10m is 4m/s, and we can rewrite the equation as:

v2 = (2r1)(2w1) = 4r1w1 = (4m/s)(5m)w1 = 20m/sw1

Therefore, the tangential speed of particle B, v2, is 20m/sw1. Since we are told that w2 = 2w1, we can substitute this into the equation to get:

v2 = 20m/s(2w1) = 40m/sw1

This means that the tangential speed of particle B is 40m/sw1, or 8m/s if w1 is equal to 1 rad/s. It is important to note that the units for tangential speed are m/s, while the units for angular speed are rad/s. Therefore, the final answer should be given in terms of m/s and rad/s.

In summary, by using the formula v = rω and taking into account the given information about tangential speed at different radii, we can calculate the tangential speed of particle B, v2. We also used the
 

1. How do you calculate angular speed from tangential speed?

In order to calculate angular speed from tangential speed, you must first determine the radius of the circle or arc that the object is moving along. Then, you can use the formula angular speed = tangential speed / radius to find the angular speed.

2. What are the units of measurement for angular speed?

Angular speed is typically measured in radians per second (rad/s) or degrees per second (°/s). However, it can also be measured in revolutions per minute (rpm) or revolutions per second (rps).

3. How does angular speed differ from linear speed?

Angular speed is a measure of how fast an object is rotating or moving along a circular path, while linear speed is a measure of how fast an object is moving in a straight line. Angular speed is rotational, while linear speed is translational.

4. Can angular speed change over time?

Yes, angular speed can change over time. An object's angular speed can increase or decrease depending on factors such as changes in tangential speed, radius, or applied torque. In circular motion, the angular speed is constant only when the tangential speed and radius are constant.

5. How is angular speed related to frequency and period?

Angular speed is directly proportional to the frequency of rotation and inversely proportional to the period of rotation. This means that as the frequency increases, the angular speed increases, and as the period increases, the angular speed decreases.

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