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Physics

Physics. Rotational Dynamics and Static Equlibrium Teacher: Luiz Izola. Chapter Preview. Torque Torque and Angular Acceleration Zero Torque and Equilibrium Center of Mass and Balance Dynamic Applications of Torque Angular Momentum Conservation of Angular Momentum Rotational Work

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Physics

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  1. Physics Rotational Dynamics and Static Equlibrium Teacher: Luiz Izola

  2. Chapter Preview Torque Torque and Angular Acceleration Zero Torque and Equilibrium Center of Mass and Balance Dynamic Applications of Torque Angular Momentum Conservation of Angular Momentum Rotational Work Vector Nature of Rotational Motion

  3. Torque (ז) Torque can be defined as the product of the tangential force (F) applied on an object by the distance (r) from the axis of rotation to the force. Torque (ז) = rF

  4. Torque (ז) Torque increase with the increase of force or the increase of distance from the axis. The torque equation from previous slide is only valid when the force applied is tangential to a circle of radius r. The more generic case is discussed next. Even though the units of torque and work are the same they represent different physical quantities. Ex: The open the door on previous slide, a tangential force is applied at a distance r from the axis of rotation. If the minimum torque required to open the door is 3.1 N.m, what force must be applied for r= 0.94 ?

  5. Torque (ז) A radial force causes zero torque. Fig a below show a radial force and fig. b show a combination of a radial and a tangential force acting on an object. General Definition of Torque (ז) ז = r (Fsin(Θ))

  6. Torque (ז) More generally, torque can be defined as the cross product between the vectors r and F. Two forces act on a wheel, as shown below. The wheel is free to rotate w/o friction, has a radius of 0.42m, and is initially at rest. Given that F1 = 12N and F2 = 9.5N, find (a) Torques caused by F1 and F2 (b) In which direction does the wheel turns as a result of these 2 forces?

  7. Torque (ז) and Angular Acceleration A tangential force applied to a mass m gives it a linear acceleration of magnitude a = F/m. The corresponding angular acceleration is α = ז/I. Prove it Newton’s Second Law for Rotational Motion ז = Iα Linear Quantity Angular Quantity m I a α F ז Ex: A light rope wrapped around a disk-shaped pulley is pulled with a force of 0.53N. Find the angular acceleration of the pulley, given that its mass is 1.3kg and its radius is 0.11m.

  8. Torque (ז) and Angular Acceleration Ex: A fisherman is dozing when a fish takes the line and pulls it with a tension T. The spool of the fishing reel is at rest initially and rotates as the fish pulls for a time t. If the radius of the spool is R, and its moment of inertia is I, find (a) the angular displacement of the spool, (b) the length of the line pulled from the spool, and (c) the final angular speed of the spool.

  9. Torque (ז) and Angular Acceleration Ex: The two blocks below have the same mass. If they are released at the same time, which lands first? (a) left, (b) right, or (c) they land at the same time. The spheres are the same in both pulleys.

  10. Torque (ז) and Angular Acceleration Ex: A person holds his outstretched arm at rest in an horizontal position. The mass of the arm is m and its length is 0.74m. When the person releases the arm, allowing it to drop freely, it begins to rotate about the shoulder joint. Find (a) the initial angular acceleration of the arm, and (b) the initial linear acceleration of the man’s hand. (hint: In calculating the torque, assume the mass of the arm is concentrated at its center. In calculating the moment of inertia, use I = mL3/3.

  11. Zero Torque (ז) and Static Equilibrium Based on the figure below, if the mass of the boy is m, the upward forces exerted by the parents must sum to mg; therefore: F1 + F2 = mg

  12. Zero Torque (ז) and Static Equilibrium This condition ensures that the net force acting on the plank is zero. However, it does not guarantee that the plank remains at rest. For example, imagine that F1 = mg and F2 = 0 for a moment where the father does not apply any force. For the plank to remain completely at rest, two conditions must be met. Conditions for static equilibrium The net force acting on an object must be zero The net torque acting on an object must be zero

  13. Zero Torque (ז) and Static Equilibrium Ex: A child of mass m is supported on a light plank by his parents, who exert the forces F1 and F2 as indicated below. Find the forces required to keep the plank in static equilibrium. Use the right end of the plank as the axis of rotation.

  14. Zero Torque (ז) and Static Equilibrium Ex: A 5.00m long board of negligible mass is supported by 2 pillars as shown below. One is at the end of the diving board and the other is 1.50m away. Find the forces exerted by the pillars when a 90kg diver stands at the far end of the board. Redraw the forces the way they really are.

  15. Zero Torque (ז) and Static Equilibrium Ex: A cat walks along a uniform plank that is 4.00m long and has a mass of 7.00kg. The plank is supported by 2 sawhorses, one is 0.44m from the left of the board and the other 1.50m from its right end. When the cat reaches the right end, the plank just begins to tip. What is the mass of the cat?

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