Posted by Joe on .
A ball (mass m = 250 g) on the end of an ideal string is moving in a circular motion as a conical pendulum. The length L of the string is 1.84 m and the angle with the vertical is 37 degrees.
a) What is the magnitude of the torque (N m) exerted on the ball about the support point?
b) What is the magnitude of the angular momentum (kg m^2/2) of the ball about the support point?
Correct Answers: a) 2.71 b) 1.32
For a I assumed 0 because there wasn't any said force. I do not know how to solve problem.
For b I used L = m*v*r where L = momentum
m = .250 kg
v = (r * g * tan 37 )^(0.5) = (L*sin 37*9.8*tan 37)^(0.5) = 2.8596
r = L * sin 37 = 1.84 * sin 37= 1.10733
Therefore L = .791 This was supposedly incorrect
a) The weight exerts a torque about the support point. It equals
Torque = M g L sin37 = 2.71 N*m^2
I am using the symbol L for string length
b) First, get the rotation period P of the ball, using equations derived at
P = 2 pi sqrt(L cos37/g) = 2.43 seconds
Ball's speed V = 2 pi L sin37/P = 2.86 m/s
The angular momentum about the support point is M*V*L
= 0.25*2.86 * 1.84 = 1.32 kg*m^2/s.