In a conical pendulum, the horizontal distance from the pivot to the mass (radius of the circular path) is given by r = L sin θ. Which option expresses this relation?

In a conical pendulum, the horizontal distance from the pivot to the mass (radius of the circular path) is given by r = L sin θ. Which option expresses this relation?

• A. r = L cos θ
• B. r = L sin θ
• C. r = L
• D. r = θ L

Answer: (B)

In a conical pendulum, the string of length L forms an angle θ with the vertical. The mass moves on a horizontal circle, so the radius of that circle is the horizontal component of the string’s length. That horizontal component is the opposite side in the right triangle formed by the string, the vertical line from the pivot, and the horizontal radius. Therefore the radius is r = L sin θ. The vertical distance from the pivot would be L cos θ. Since θ is measured from the vertical, the horizontal distance naturally comes from sine. If θ were defined from the horizontal, the relation would be r = L cos θ. This geometric projection is why r = L sin θ correctly expresses the radius.

In a conical pendulum, the string of length L forms an angle θ with the vertical. The mass moves on a horizontal circle, so the radius of that circle is the horizontal component of the string’s length. That horizontal component is the opposite side in the right triangle formed by the string, the vertical line from the pivot, and the horizontal radius. Therefore the radius is r = L sin θ. The vertical distance from the pivot would be L cos θ. Since θ is measured from the vertical, the horizontal distance naturally comes from sine. If θ were defined from the horizontal, the relation would be r = L cos θ. This geometric projection is why r = L sin θ correctly expresses the radius.