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Lect_22 - ACT Spheres Two spheres have the same radius and...

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1 Lecture 22 Torque ACT: Spheres Two spheres have the same radius and equal masses. One is made of solid aluminum and the other is a hollow shell of gold. Which one has the biggest moment of inertia about an axis through its center? A. Solid Al B. Hollow Au C. Both the same Hollow gold Solid aluminum Mass is further away from the axis 2 tan F r mr α = An intuitive approach to torque A particle of mass m is constrained by a massless rod of length r to move in circles about point P. A force F is applied on the particle.This is the only force applied on it. What is the angular acceleration of the system? r F m F r F tan F tan produces a tangential acceleration: tan tan F ma = I t a r α = tan F m r α = I τ α = P Torque tan F r τ = Directions: Both and point out of the screen. α G r F × G G τ α = z z I r F τ = × G G G θ sin Fr r F θ = = × G G Newton’s second law for rotations r F τ = × G G G For each force on a system, the torque depends on the point on which it is applied τ τ α = = net, i, all forces z z z I The angular acceleration will be the result of adding all these torques: τ G G net Note: In general,

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