What is the speed of the ball when it is in circular motion?

A small metal ball is suspended from the ceil-

ing by a thread of negligible mass. The ball

is then set in motion in a horizontal circle so

that the thread describes a cone.

The acceleration of gravity is 9.8 m/s^2 :





l=1:5 m

m=6.8 kg

angle=24degree



What is the speed of the ball when it is in

circular motion? Answer in units of m/s.What is the speed of the ball when it is in circular motion?What do you mean by I=1:5m? I will assume the thread is 1.5m long.



The ball is subjected to two forces: gravity (Fg) and centrifugal force (Fc).



Fg = m*g

Fc = m*w^2*r where

r is the radius of rotation

w is radial speed in rad/s



The angle a made by the thread is such that



sin(a)/cos(a) = Fc/Fg = m*w^2*r / m*g = w^2*r/g



Now the radius r of the circle made by the ball is equal to sin(a)*l so the formula becomes



sin(a)/cos(a) = w^2*sin(a)*l/g

1/cos(a) = w^2*l/g

w = sqrt(g/(l*cos(a)) = sqrt(9.8/(1.5*cos(24)) = 2.67 rad/s



So the radial speed is 2.67 rad/s (0.42 rev per second).

And velocity is equal to

v = w*r = 2.67 rad/s * sin(24)*1.5 = 1.63m/sWhat is the speed of the ball when it is in circular motion?I'm assuming the 24 deg is string angle from the vertical, not the horizontal.

The ball moves in a circle of radius r = 1.5m * sin(24 deg)

There are two equal-magnitude opposing accelerations along the tangent to the arc the ball makes with the vertical at the location of the ball.

The inward gravitational accel

Ai = g * sin(24 deg).

The outward centrifugal acceleration

Ao = cos(24 deg) * v^2 / r.

Ao = Ai, so

v^2 = Ai * r / cos(24 deg), and

v = sqrt(g * 1.5m * (sin(24 deg))^2 / cos(24 deg))

You can compute the period T as 2 * pi * r / v.

EDIT: Steve's answer is correct and brief, but in deriving it from forces he needlessly involves M, and part of the brevity is the omission of a definition of r. I prefer self-sufficiency.What is the speed of the ball when it is in circular motion?I like this answer better:

MV虏/r = Tsin24掳 where T is the tension in the thread = Mg/cos24掳

Canceling and cross multiplying gives

V虏 = rg*tan24掳 (m/s)虏

Now knowing V, T = 2蟺 *r/ V sec