The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Two questions on circular motion

1. A particle is attached by means of a light, inextensible string to a point 0.40m above a smooth, horizontal table. The particle moves on the table in a circle of radius 0.30m with angular velocity ω. Find the reaction on the particle in terms of ω. Hence find the maximum angular velocity for which the particle can remain on the table.

So for this question I've figured out that R=mg−0.4mω2R=mg-0.4m\omega^2, but how do you find the maximum angular velocity?

2. A particle of mass 0.30kg moves with an angular velocity of 10 rad/s in a horizontal circle of radius 20cm inside a smooth hemispherical bowl. Find the reaction of the bowl on the particle and the radius of the bowl.

I got the reaction force, but how do you go about finding the radius of the bowl?
Original post by yangg
1. A particle is attached by means of a light, inextensible string to a point 0.40m above a smooth, horizontal table. The particle moves on the table in a circle of radius 0.30m with angular velocity ω. Find the reaction on the particle in terms of ω. Hence find the maximum angular velocity for which the particle can remain on the table.

So for this question I've figured out that R=mg−0.4mω2R=mg-0.4m\omega^2, but how do you find the maximum angular velocity?

2. A particle of mass 0.30kg moves with an angular velocity of 10 rad/s in a horizontal circle of radius 20cm inside a smooth hemispherical bowl. Find the reaction of the bowl on the particle and the radius of the bowl.

I got the reaction force, but how do you go about finding the radius of the bowl?


I'll give you a hint for part 1. What happens to the reaction force when 0.4mω20.4m\omega^2 exceeds mg? (assuming your calculation for R is even correct, I haven't checked it)
(edited 9 years ago)
Original post by yangg
1. A particle is attached by means of a light, inextensible string to a point 0.40m above a smooth, horizontal table. The particle moves on the table in a circle of radius 0.30m with angular velocity ω. Find the reaction on the particle in terms of ω. Hence find the maximum angular velocity for which the particle can remain on the table.

So for this question I've figured out that R=mg−0.4mω2R=mg-0.4m\omega^2, but how do you find the maximum angular velocity?

2. A particle of mass 0.30kg moves with an angular velocity of 10 rad/s in a horizontal circle of radius 20cm inside a smooth hemispherical bowl. Find the reaction of the bowl on the particle and the radius of the bowl.

I got the reaction force, but how do you go about finding the radius of the bowl?



Part 1.
Take another look at this.
1. The centripetal force is mrω² , but r is not 0.4m
2. If T is the tension in the string, this centripetal force is Tcos θ where θ is the angle the string makes with the horizontal.
3. mg is balanced by R and the vertical component of T.
(edited 9 years ago)
Reply 3
Avatar for yangg
yangg
OP
2
Original post by Stonebridge
Part 1.
Take another look at this.
1. The centripetal force is mrω² , but r is not 0.4m
2. If T is the tension in the string, this centripetal force is Tcos θ where θ is the angle the string makes with the horizontal.
3. mg is balanced by R and the vertical component of T.


I've got that far. I just can't figure out the last bit.


Posted from TSR Mobile
Reply 4
Avatar for patot
patot
Original post by yangg
I've got that far. I just can't figure out the last bit.


Posted from TSR Mobile


Consider the value of R in the case of maximal possible angular velocity.
(edited 9 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you