Learn How to Read Graphs: Angular Speed & Tangential Speed

[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!

 

[tiny-tim]

welcome to pf!

hi scruffles! welcome to pf!

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

 

[scruffles]

Thanks for your reply!

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

 

[tiny-tim]

b) yes

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

 

[scruffles]

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

 

[tiny-tim]

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

why 5 ?

 

[scruffles]

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

 

[tiny-tim]

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

 

[scruffles]

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