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

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Presentation on theme: "Up to this point, balanced Forces meant no acceleration…. 100 N Balanced Forces? Yes! No Acceleration? It will accelerate in a spin!"— Presentation transcript:

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

2 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?

3 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: N  m

4 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.

5 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?

6 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?

7 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. 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!

8 The angular acceleration of an object will depend directly upon the net torque, but inversely upon the rotational inertia of the object:  = τ I therefore  τ = I  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!

9 Rotational Inertia, also called moment of inertia, (kg  m 2 ) 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?

10 A wheel with a rotational inertia of.270 kg  m 2 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 kg  m 2. 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?

11 F1F1 F2F2 This meterstick is at rest on frictionless ice when F 1 and F 2 strike it simultaneously. F 1 and F 2 are both 3.85 N. F 1 strikes at the m mark while F 2 strikes at the cm mark. Will the stick rotate and, if so, will it be clockwise or counterclockwise?

12 If the meterstick in the previous problem has a rotational inertia of kg-m 2, 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/s 2, what must be the moment of inertia of the door?


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