# Angular Speed of a bob of mass

David Swift
1. Relevant information

A bob of mass 0.5kg is attached to one end of a light inextensible string of length 0.500 m, whose other end is attached to a fixed pivot. The bob performs uniform circular motion in a horizontal plane, with the string making an angle of 30.0° with the vertical.

2. Question

What is the angular speed of this circular motion?
Hint: you can begin by using Newton's second law in the vertical direction to find the tension in the string.)

## The Attempt at a Solution

Tension in string
F Cos 30 = 0.5 x 9.81
F = (0.5 x 9.81) / Cos 30
F = 5.66N

Radius of circle must be 0.5x Sin 30 = 0.25m

F = mass x radius x angular speed^2
Angular speed = Sqrt ( 5.66 / (0.5 x 0.25))
Angular speed = 6.72 rad s^-1

Have I done this right?

## Answers and Replies

Mentor
Tension in string
F Cos 30 = 0.5 x 9.81
F = (0.5 x 9.81) / Cos 30
F = 5.66N

Radius of circle must be 0.5x Sin 30 = 0.25m

F = mass x radius x angular speed^2
Angular speed = Sqrt ( 5.66 / (0.5 x 0.25))
Angular speed = 6.72 rad s^-1

Have I done this right?
Almost. Realize that the centripetal acceleration is horizontal, so only the horizontal component of the tension provides the centripetal force.

David Swift
Almost. Realize that the centripetal acceleration is horizontal, so only the horizontal component of the tension provides the centripetal force.
I am not sure what you mean by that. Have I used a wrong equation?

Mentor
I am not sure what you mean by that. Have I used a wrong equation?
When you used ##F = m \omega^2 r##, you used the entire tension as the force. But only the horizontal component of the tension creates the centripetal acceleration.

David Swift
When you used ##F = m \omega^2 r##, you used the entire tension as the force. But only the horizontal component of the tension creates the centripetal acceleration.
F(x) = ((m x g ) x Xcomponent / length
F (x) = (0.5 x 9.81 x 0.5 sin 30 ) / 0.5m = 2.22 rad s^-1

Science Advisor
Homework Helper
Gold Member
F(x) = ((m x g ) x Xcomponent / length
You seem to have taken a step backwards. Your original equation for tension(F) was correct:
F Cos 30 = 0.5 x 9.81
Doc Al is telling you this equation is wrong (assuming F is still the tension):
F = mass x radius x angular speed^2
Please try to post a correct version.