Questions: Balls are attached to light rods and can move in horizontal circles as shown in the figure (Figure 1) r m F r 2m 2F 2r m F 2r 2m 2F 1 2 3 4 Rank in order, from smallest to largest, the torques τ1 to τ4 about the centers of the circles. To rank items as equivalent, overlap them. Reset Help τ1 τ2 τ3 τ4 the smallest torque the largest torque

Balls are attached to light rods and can move in horizontal circles as shown in the figure (Figure 1)

r m F

r 2m 2F

2r m F

2r 2m 2F

1 2 3 4

Rank in order, from smallest to largest, the torques τ1 to τ4 about the centers of the circles.

To rank items as equivalent, overlap them.

Reset Help

τ1 τ2 τ3 τ4

the smallest torque    the largest torque
Transcript text: Balls are attached to light rods and can move in horizontal circles as shown in the figure (Figure 1) $r$ $m$ $F$ $r$ $2m$ $2F$ $2r$ $m$ $F$ $2r$ $2m$ $2F$ 1 2 3 4 Rank in order, from smallest to largest, the torques $\tau_1$ to $\tau_4$ about the centers of the circles. To rank items as equivalent, overlap them. Reset Help $\tau_1$ $\tau_2$ $\tau_3$ $\tau_4$ the smallest torque | | | the largest torque
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Solution

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Solution Steps

Step 1: Define the formula for torque

Torque (τ) is the rotational equivalent of linear force. It is defined as the cross product of the force (F) and the distance (r) from the pivot point to where the force is applied. In these cases, the force and the radial vector are perpendicular, simplifying the calculation to: τ = rF

Step 2: Calculate the torque for each case
  • Case 1: τ₁ = rF
  • Case 2: τ₂ = r(2F) = 2rF
  • Case 3: τ₃ = (2r)F = 2rF
  • Case 4: τ₄ = (2r)(2F) = 4rF
Step 3: Rank the torques

From smallest to largest torque, the ranking is τ₁, τ₂ and τ₃ (equal), τ₄.

Final Answer:

1, 2&3, 4

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