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# Circular Motion watch

1. Need some help with this question please.

"A sphere of mass m is spun in a circular path on the end of a string 1.0 m long. If the string makes an angle of 20° with the vertical, as shown in the figure, what is the horizontal tangential speed of the sphere? (Assume acceleration due to gravity is g=10 ms-2)"

This is what I did:

Tcos(20)=W=mg
Tsin(20)=ma

tan(20)=a/g
a=10*tan(20)
a=3.64

a=v^2/r
v^2=3.64 *1

v=1.91 ms^-1

Isn't linear speed the same as horizontal tangential speed?

2. Not completely sure what it means by horizontal tangential speed but my guess is that it would be the horizontal component of the linear (tangential) speed so you need to find the horizontal component of the speed you've found.
3. But don't I need another angle for that? Or is it simply a case of doing 1.91 * cos(20)?
4. (Original post by john.miguel)
But don't I need another angle for that? Or is it simply a case of doing 1.91 * cos(20)?
Yup that looks right. Do you know what the answer should be?
5. (Original post by suneilr)
Yup that looks right. Do you know what the answer should be?
Unfortunately no, but I did post this question on Yahoo Answers and:

As you can see the poster used sin instead of cos to find the horizontal component, I've never been good with when to know which one to use, sin or cos. But I take it he/she is wrong? And it is cos(20) that I have to use?
6. (Original post by john.miguel)
But don't I need another angle for that? Or is it simply a case of doing 1.91 * cos(20)?
I think it is.
7. (Original post by john.miguel)
Unfortunately no, but I did post this question on Yahoo Answers and:

As you can see the poster used sin instead of cos to find the horizontal component, I've never been good with when to know which one to use, sin or cos. But I take it he/she is wrong? And it is cos(20) that I have to use?
Can you post the diagram that was given? Is 20 deg the angle between the string and upper vertical or lower vertical?
8. (Original post by suneilr)
Can you post the diagram that was given? Is 20 deg the angle between the string and upper vertical or lower vertical?
Here it is:

9. (Original post by john.miguel)
Here it is:

Oh right. Damn I thought the particle was moving in a vertical plane. Ok yeah the horizontal tangential speed would just be the tangential speed in the horizontal plane ie the linear speed, so you don't need to bother with the cos or sin at the end.
10. (Original post by suneilr)
Oh right. Damn I thought the particle was moving in a vertical plane. Ok yeah the horizontal tangential speed would just be the tangential speed in the horizontal plane ie the linear speed, so you don't need to bother with the cos or sin at the end.
Great! Thank you very much =D Left +rep.
11. Np, its good to see I can still do some physics lol... Thanks

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