Rpm Picture
Rpm Picture
What is tension in the string? What is the ball's angular velocity, in rpm?
A conical pendulum is formed by attaching a 0.800 kg ball to a 1.00 m-long string, then allowing the mass to move in a horizontal circle of radius 30.0 cm. The picture of the ball and string tied together ans swinging in a circle looks like a cone.
What is tension in the string?
What is the ball's angular velocity, in rpm?
if (p) is the semi-angle of this at top point (vertex)
then tension T directed at hand can be resolved along the centripetal force direction and counter to its weight like
T cos (90- p) = mv^2/r = m w^2 r = T sin p
(needed to be in circle)
T sin (90 -p) = mg = T cos p
tan (p) = w^2* r / g (w is angular freq)
r is radius, L is length so sin p = r / L = 0.3/1=0.3
cos p = sqrt(1 - 0.09) =0.9539
T = mg / cos p = 0.80*9.8 / 0.9539 = 8.218 Newton
w^2 r / g = tan p = 0.3 / 0.9539 = 0.3144
w^2 = 0.3144 *9.8 /0.3 = 10.27
w= 3.20 rad/sec = 3.20 rad / (1/60) min = 3.20*60 rad/min
2 pi radc = 1 revol
w = 3.20*60 /2 pi = 30.57 rpm
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