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**It will accelerate in a spin!**

Up to this point, balanced Forces meant no acceleration…. 100 N Balanced Forces? No Acceleration? Yes! It will accelerate in a spin! 100 N

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**Rotational Dynamics and Torque**

A net force will cause and object to accelerate in one dimension, but what about rotational acceleration? Would a Force exerted at .5r from the center produce the same rotational acceleration around the center as……. ….. the same force exerted at r from the center?

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**Forces that are not concurrent (same point) are called Parallel Forces.**

Parallel Forces exert Torque on an object. Torque is the product of the Parallel Force and the torque arm (lever arm) the force acts through. τ = r x F Units: Nm

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What torque is exerted by a 55 kg bike rider who puts all of his weight straight down on each pedal (one pedal at a time) if each pedal is 17 cm from the center of the sprocket? What force needs to be exerted on the end of a torque wrench that is 35.0 cm long in order to tighten a bolt to 80.0 Nm? Explain why doorknobs are generally placed toward the side of a door instead of in the middle of the door.

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**A force of 5. 00 N is used to turn a doorknob that has a diameter of 6**

A force of 5.00 N is used to turn a doorknob that has a diameter of 6.70 cm. What torque does this exert? A torque of 3.25 Nm is required to pull open a certain door. What force must be used to open this door if the knob is located 75.0 cm away from the hinge? The mass exerts a torque of 23.0 Nm on the wheel which has a diameter of 45.0 cm. How much is the attached mass that produces this torque?

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**The wheel on a car is held in place by four nuts**

The wheel on a car is held in place by four nuts. Each nut should be tightened to 94.0 N∙m of torque to be secure. If you have a wrench with a handle that is m long, what minimum force do you need to exert perpendicular to the end of the wrench to tighten a nut correctly? Bob and Ray push on a door from opposite sides. They both push perpendicular to the door. Bob pushes 0.63 m from the door hinge with a force of 89 N. Ray pushes 0.57 m from the door hinge and the door does not move. What force is Ray pushing with?

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**Rotational Inertia and Net Torque**

An object will not start to spin unless a net torque acts upon it. A net torque would produce an angular acceleration. An object spinning at a constant rate will accelerate if the mass is redistributed farther or closer to the axis of rotation. Meterstick Demo! Rotational Inertia is the resistance of a rotating object to changes in its rotational velocity-- it depends on mass, distribution of mass, and the axis of rotation!

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The angular acceleration of an object will depend directly upon the net torque, but inversely upon the rotational inertia of the object: = τ I τ = I therefore This is the rotational equivalent of Newton’s Second Law (F = ma) for angular motion! Rotational Inertia takes into account both the shape, the mass and the rotation of a rotating object!

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Rotational Inertia, also called moment of inertia, (kgm2) depends upon the mass and the axis of rotation: The farther the mass is concentrated from the axis of rotation, the more rotational inertia Ring and disk of same mass and same radius--- Will they reach the bottom at the same time?

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**A wheel with a rotational inertia of**

A wheel with a rotational inertia of .270 kgm2 is accelerated from rest to 35.0 rad/s in 10.0 s. What torque is required to accomplish this? A force of 25.0 N is applied to a disk with a radius of .300 m that is initially rotating at 38.0 rad/s. The disk is stopped after having rotated 95.0 radians. What is the rotational inertia of this disk? A torque of 32.0 Nm is used to accelerate a sphere of rotational inertia 175 kgm2. If the sphere is accelerated to 8.66 rad/s in 20.0 s, what must have been the original angular velocity of the sphere?

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F1 F2 This meterstick is at rest on frictionless ice when F1 and F2 strike it simultaneously. F1 and F2 are both 3.85 N. F1 strikes at the m mark while F2 strikes at the cm mark. Will the stick rotate and, if so, will it be clockwise or counterclockwise?

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If the meterstick in the previous problem has a rotational inertia of kg-m2, what will be its angular acceleration? Bob and Ray push on a door from opposite sides. They both push perpendicular to the door. Bob pushes 0.63 m from the door hinge with a force of 89 N. Ray pushes with a force of 98 N at a point 0.57 m from the door hinge and the door does not move. If the door gains an angular acceleration of rad/s2, what must be the moment of inertia of the door?

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