# Learn How to Read Graphs: Angular Speed & Tangential Speed

• scruffles
In summary, the black curve represents the position of a spot on the x-axis projection of a spinning wheel. The blue curve represents the velocity of that spot. The angular speed of the wheel is 0.4 seconds. The tangential speed of the wheel is 31.4 cm, assuming the full radius of the wheel is represented in this projection. The x-projection does not have an angular acceleration at any time on the graph.
scruffles

## Homework Statement

The black curve represents the position of a spot on the x-axis projection of a spinning wheel.

a) Which curve represents the velocity of that spot? blue
b) What is the angular speed of the wheel?
c) What is the tangential speed of the wheel, assuming the full radius of the wheel is represented in this projection.
d) Does the x-projection have an angular acceleration at any time on the graph? Explain.

## The Attempt at a Solution

I have no idea how to read this graph. The only thing I can guess is that a) would be the blue line? Please help!

welcome to pf!

hi scruffles! welcome to pf!
scruffles said:
a) Which curve represents the velocity of that spot? blue
b) What is the angular speed of the wheel?
c) What is the tangential speed of the wheel, assuming the full radius of the wheel is represented in this projection.
d) Does the x-projection have an angular acceleration at any time on the graph? Explain.

(a) correct
(b) hint: how long does it take to go round 360° ?
(c) hint: how far does it go when it goes round 360° ?
(d) sorry, i don't understand the question

So for b) would the angular speed would be .4s?
c) would it be 0? since it goes from -8 to 8 ?

b) yes

c) no (how much tape would you have to wind round the wheel?)

would i use C=2pir?
c= 2(3.14)(5) = 31.4 cm?

scruffles said:
would i use C=2pir?
c= 2(3.14)(5) = 31.4 cm?

why 5 ?

because the diameter of the wheel is 10? so half of it would be the radius of 5?

but the graph shows x going from -10 to 10, so half of that would be 10 ?

you're right, my mistake. Thanks for your help!

## 1. What is angular speed?

Angular speed is the rate at which an object rotates or travels around a central point. It is measured in radians per unit time.

## 2. How is angular speed different from tangential speed?

Angular speed measures the rotation of an object, while tangential speed measures the linear motion of an object along a circular path. Tangential speed is calculated by multiplying the angular speed by the radius of the circle.

## 3. How do you read a graph of angular speed?

A graph of angular speed typically plots the angular speed on the y-axis and time on the x-axis. The slope of the line on the graph represents the angular acceleration, while the area under the curve represents the change in angular displacement.

## 4. What factors can affect angular speed?

Some factors that can affect angular speed include the mass of the rotating object, the radius of the circle, and the magnitude of the applied torque. Friction and air resistance can also affect the angular speed of an object.

## 5. How can learning about angular speed and tangential speed be useful?

Understanding angular speed and tangential speed can be useful in various fields, such as physics, engineering, and astronomy. It can help in calculating the motion of rotating objects, determining the speed and direction of celestial bodies, and designing machines that involve circular motion.

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