Classical Mechanics - Pendulum


The figure above represents a point mass m attached to the ceiling by a cord of fixed length l. If the point mass moves in a horizontal circle of radius r with uniform angular velocity ω, the tension in the cord is

A. mgr / l
B. mg cos(θ/2)
C. mωr sin(θ/2)
D. m(ω²r² +g²)½
E. m(ω4r2 +g2 )½
(GR8677 #37)
Solution:

Horizontal components:
T sin (θ/2) = Fa = mv² / r = ²r

Vertical components:
T cos(θ/2) = mg

The magnitude of T:
T² = [T sin(θ/2)]² + [T cos(θ/2)]² = (²r)² + (mg
T = m(ω4r2 +g2 )½

Answer: E

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