Force Faceoff Worksheet

Rotational Dynamics & Equilibrium Mastery

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Section 1: The Dynamic Translation

Map the linear dynamic concept to its rotational twin.

Linear Dynamics

1. Mass (\(m\))

2. Net Force (\(\sum F\))

3. Accel direction (+)

Rotational Dynamics

A. Counter-Clockwise (+)

B. Moment of Inertia (\(I\))

C. Net Torque (\(\sum \tau\))

Section 2: Rod Analysis

Identify which forces produce Zero Torque on the rod below and explain why.

F_A F_B F_C

Force A:

Force B:

Force C:

*Which force will actually rotate the rod?

Section 3: Inertia Thinking

Explain, using the concepts of mass distribution and Moment of Inertia, why a solid oak disk is easier to start spinning than a hollow steel hoop of the same mass and radius.

Section 4: Square Torque Synthesis

A square plate with side length \( L = 0.60 \text{ m} \) is pinned at its center.

F1=10N

F2=20N

F3

F4=30N

A. Find individual Torques:

τ1 = _________________________

τ2 = _________________________

τ4 = _________________________

B. Net Torque Sum:

Section 5: The Hexagon Challenge

Determine the Net Torque on the hexagonal nut using \( r_{side} = 0.03 \text{ m} \) and \( r_{vertex} = 0.035 \text{ m} \).

F1=40N F2=20N F3=100N F4=10N

NET TORQUE MAGNITUDE & DIRECTION (+/-)

Section 6: Advanced Equilibrium

Problem 1: The massy beam sign

SUM OF TORQUES = 0

A uniform beam of mass \( M = 8.0 \text{ kg} \) and length \( L = 4.0 \text{ m} \) is pivoted at a wall. A sign of mass \( m = 12 \text{ kg} \) hangs at \( 3.0 \text{ m} \) from the pivot. A rope is attached at the far right end and pulls up at an angle of \( 30^\circ \).

Calculate the Tension (T) in the rope required for static equilibrium. (\(g = 10 \text{ m/s}^2\))

Conceptual Conclusion

In any equilibrium system, does the choice of pivot point matter for the final calculation? Why do engineers often pick a pivot where there is an unknown force?

Force and Torque Worksheet Final Updated v1

Force and Torque Worksheet Final Updated v1

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