Number of revolutions within 4 seconds

[ch2kb0x]

Homework Statement

There is an attachment for the picture. question is, How many revolutions does the object make during the first 4 s?

Homework Equations

The Attempt at a Solution

I attempted to solve this by dividing 20 by 2pi, but apparently, that was wrong. Any help?

 

[alphysicist]

Hi ch2kb0x,

Homework Statement

There is an attachment for the picture. question is, How many revolutions does the object make during the first 4 s?

Homework Equations

The Attempt at a Solution

I attempted to solve this by dividing 20 by 2pi, but apparently, that was wrong. Any help?

Check your units: when you did the division, and divided the units of 20 and 2pi, did you get radians (or revolutions)? Or was time not cancelled?

What part, or property, of this graph would represent the angle through which the object rotates?


(As an analogy, if you had a v vs. t graph, how could you use the graph directly to find the distance travelled? It's the same idea here.)

 

[ch2kb0x]

its basically a line going up like a y=x graph, all the way up to 20 omega (rad/s) till 2 seconds.
And at t=2 seconds, this is when it stays constant the rest of the way (line stays horizontal) at
20 omega(rad/s)

 

[alphysicist]

its basically a line going up like a y=x graph, all the way up to 20 omega (rad/s) till 2 seconds.
And at t=2 seconds, this is when it stays constant the rest of the way (line stays horizontal) at
20 omega(rad/s)

Right, and what about the graph gives the angular displacement they are looking for?

For example, the slope of the curve (of an omega vs time graph) gives the acceleration. What gives the angular displacement?

 

[ch2kb0x]

erm...that was the only graph I was given. =\

 

[alphysicist]

erm...that was the only graph I was given. =\

That's the one I'm talking about. If you take the graph you are given and look at the slope of the line, you will get the acceleration.

What on the graph do you look at if you want to find the angle it rotates?

 

[dib_elias]

If I understand your description correctly, you have angular velocity plotted on the y-axis and time on the x axis. If that is so, the area under this graph should be equal to the angular displacement of the particle, theta. Based on your description this comes out to
Area=theta=1/2*2*20+2*20=60rad
To determine the number of revolutions just divide this angular displacement by 2pi.
#rev=60rad/6.28rad/rev=9.55rev