Physics Ninja: Torque and Equilibrium of Rigid Bodies

Compare forces and torque with a door example; see how torque depends on force magnitude, center of mass, pivot position, and the angle of application to achieve rotation and equilibrium.

Torque is the tendency of a force to rotate an object. If F is perpendicular to r, torque magnitude equals |r||F|; increase either to raise torque; torque is a vector.

Learn torque as a plane vector, compute magnitude from the lever arm to the line of action and the angle between force and radius, and assign sign for rotation.

Learn how multiple forces produce torque on a system, calculate torque as distance to the pivot times force with sign, and determine equilibrium when net torque is zero.

Define torque for rigid bodies using RF sin theta, the shortest distance to the line of action, and the perpendicular component of the force.

Explore torque behavior: zero torque for angles 0 or 180 degrees, maximum torque for 90 or 270 degrees; equal magnitudes arise with equal forces, emphasizing the angle theta.

Explore torque calculations using the perpendicular component of force and the moment arm D, the perpendicular distance from the axis to the line of action of the force.

Compare torques from wrenches of different lengths and forces using torque = r f sin theta, and identify case e as the largest through angle and perpendicular component reasoning.

Compute torques from three forces on a 2-meter swinging door, using the wedge at 1.5 meters to balance torques and show the wedge force must be zero for rotational equilibrium.

Explore the center of mass and how torque determines equilibrium, using a baseball bat and pivot examples to demonstrate balancing and calculating center of mass in varied shapes.

Determine the center of mass for symmetric shapes on planes of symmetry under constant density to assess balance. Note it may lie inside or outside the object.

Compute the center of mass for two particles as m1 x1 plus m2 x2 divided by m1 plus m2. It shifts toward the heavier mass and depends on the origin.

Compute the center of mass for two masses using their positions and masses; the result is 4 m and the center of mass remains invariant under coordinate system changes.

Represent the sphere and rod as point masses at their centers of mass and apply the center-of-mass formula to determine the system's center, then balance it with a pivot.

calculate the center of mass for multiple objects in two dimensions using x and y coordinates, and extend to three dimensions with a position vector from the origin.

Calculate the center of mass for three masses 1.2, 2.5, and 3.4 kg at the vertices of an equal lateral triangle, edge 140 cm, using a two-dimensional coordinate system.

Calculate the center of mass of a rectangular frame with missing corners by dividing it into four segments, assigning masses by length, and combining x and y coordinates.

Explore static equilibrium by applying free body diagrams to ensure net force and net torque equal zero, using center of mass, weight, and normal force to analyze pivots.

Delve into static equilibrium by balancing forces and torques to keep objects at rest and not rotating, with examples like a book, a hanging sign, and a ladder.

Analyze a light rod with equal opposite forces to confirm force equilibrium but not torque equilibrium, illustrating how net torque depends on pivot placement.

Analyze a seesaw with a 50 kg plank pivoted at its center of gravity, balancing 80 kg father and 40 kg daughter; compute the normal force and dad’s position.

Choose any pivot point to calculate torques on a rigid body in equilibrium; the location is arbitrary, but some points simplify calculations and others yield zero torque.

Compute torque on a beam by using the center of gravity (center of mass) or by summing small-mass torques; torque equals total mass times g times distance to the pivot.

Explore how the center of gravity equals the center of mass and compute it via weighted positions to simplify torque calculations for static equilibrium.

Analyze torque on a uniform ladder from gravity using the center of gravity and the angle between r and the force, noting the sign for clockwise rotation.

Draw sketches and free body diagrams, place forces at their points of application, resolve into components in a convenient coordinate system, and apply torque and equilibrium equations.

Examine a uniform ladder against a smooth wall, with gravity at the center, normal forces at ground and wall, and friction opposing motion to select the correct free body diagram.

Explore a ladder leaning against a smooth wall, analyze the free-body forces, and derive the minimum angle for equilibrium given a ground friction coefficient of 0.4.

Construct a free-body diagram and apply torque balance for a ladder against a wall, deriving tan theta = 1/(2 mu_s) and theta about 51 degrees when mu_s = 0.4.

Solve a center-of-mass problem by applying a free-body diagram, balancing the weight and two normal forces about a pivot to find the center of mass position x.

Illustrates torque and equilibrium for a horizontal rigid bar weighing 100 N, hinged at the wall and held by a ceiling spring scale at 30 degrees, finding tension.

Analyze the net torque of a three-spoke wheel by drawing a free body diagram for each spoke, using angles 90°, 30°, and 120°, summing torques to zero with counter-clockwise positive.

Explore a horizontal beam torque problem by building a free body diagram, applying torque and force balance to solve for the cable tension and the wall reaction in static equilibrium.

Explain how equilibrium requires zero net force and torque, and compare stable, neutral, and unstable equilibria using center of gravity and pivot ideas.

Explore how gravity provides restoring torque about the pivot to keep a polygon in stable equilibrium, as the center of gravity and lever arm determine stability.

Explore stable and unstable equilibrium by analyzing torque about a pivot. See barstools, cars, and a bus illustrate how center of gravity determines topple risk.

Compute the net torque on two connected wheels by summing tangential forces about the center; with theta 90 degrees, the magnitude equals four F r.

Compare torques about a pivot using the torque formula tau = r F sin theta, considering distance, force, and angle; case b matches the reference torque.

Compute the center of mass for a rectangle with a missing corner using x and y coordinates, mass distribution, and decomposition strategies including the negative mass method.

Calculate the torque about the origin for the square under F1 and F2 using the r vector, line of action, and the perpendicular distance.

Solve two torque problems by balancing torques and forces on a bar with weights W, finding tensions T and T-2 and pivot reactions via a free body diagram, achieving equilibrium.

Solve torque and equilibrium by analyzing a beam with tension and weights, computing the tension and reaction forces from a free-body diagram using angle-based components.

Analyze torque and equilibrium on a two-supported uniform beam as a ninja walks across, showing how support forces vary, tipping points, and how to reposition a support to reach the end.

Balance the torque about the hammer pivot, equating the nail's 500 N torque (0.08 m, 60°) with the handle torque (0.3 m). Compute the result as about 116 N.

an analysis of the minimum horizontal force to pull a wheel over a curb, comparing center and top-edge, using torque about the curb edge and wheel weight to reach equilibrium.

Explore the book stacking overhang problem using center of mass and torque to assess stability and maximum overhang for 1–4 blocks, including exceedance beyond the length of a block.

Analyze equilibrium of two identical marbles in a three-centimeter-wide jar by constructing free-body diagrams, applying torque about a pivot, and solving for the contact forces between marbles and walls.

Design a decorative mobile and determine weights A, B, and C and string tensions by drawing free-body diagrams and applying torque and vertical force equilibrium about a pivot.

Treat the square with a circular cutout as two masses using the negative-mass method to compute center of mass and show the shift toward the top diagonal of 0.061 a.