Find angle of string for rotating bob with given radius

[jinhuit95]

Homework Statement

A small bob is suspended from a fixed point by a string 0.50m long. It is made to rotate in a horizontal circle of radius 0.40m, the center of this circle being vertically below the point of support. Find the angle of inclination of the string, with respect to the vertical.

Homework Equations

The Attempt at a Solution

What I did was to draw the diagram out and i used tan θ = 0.4/0.5. θ=38.7(1d.p.) Am I correct??

 

[tiny-tim]

welcome to pf!

hi jinhuit95! welcome to pf!

A small bob is suspended from a fixed point by a string 0.50m long. It is made to rotate in a horizontal circle of radius 0.40m, the center of this circle being vertically below the point of support.
…
i used tan θ = 0.4/0.5

no, tan = opp/adj (opposite over adjacent), but .5 isn't the adjacent side, is it?

 

[jinhuit95]

Yes yes I solved it already but now how do I find angular velocity?? Do I use 2pi/t?? The thing is I don't know how to find t.

 

[tiny-tim]

you'll need to use F_total = ma where "a" is the centripetal acceleration

 

[jinhuit95]

Okay! I have another question. Angular velocity is 2pi/t?? T is revolution per sec or radian per sec??

 

[tiny-tim]

angular velocity is always radians per second

so if the period is T seconds, that means it goes 2π radians in T seconds …

ie 2π/T radians per second ​

(but you won't need to find T … the centripetal acceleration formula already has the angular velocity, ω = v/r, in it )

 

[jinhuit95]

So if they give u period in terms of revolutions per sec, you have to change it to radians per sec??

 

[tiny-tim]

So if they give u period in terms of revolutions per sec, you have to change it to radians per sec??

revolutions per second isn't a period, it's an angular velocity

and yes, you must convert angular velocity to radians (not revolutions) per time, or the formulas won't work

 

[Ratch]

Wrong post, sorry.