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PHYS2001_Ch. 9

# PHYS2001_Ch. 9 - Ch 9 Rotational Dynamics 9.1 Torque Forces...

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Ch. 9 Rotational Dynamics 9.1 Torque Forces cause linear accelerations: ma F = But what causes angular accelerations, α ? In other words, what is the rotational analog of force ? It’s Torque ! F r a a a × = τ θ sin rF = x F r θ Axis of rotation r is the distance from the axis of rotation to the point of contact of the force. θ is the angle between r and F . Torque is positive for ccw rotations and negative for cw rotations. Units? [Force x distance] [N·m]

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James finds it difficult to muster enough torque to turn the stubborn bolt with the wrench. He has a section of rope which he ties to the wrench as shown and pulls just as hard. Will the torque be increased? Yes No 50% 50% Clicker Question 1. Yes 2. No
The figure below shows the top view of a heavy door that is free to rotate about an axis along its right edge. Which of the following diagrams represents the best location and orientation of an applied force that is most effective in rotating the door? The magnitude of the force, F, in each case is the same. A B C D E 20% 20% 20% 20% 20% x F x x F F x F x F 1. A 2. B 3. C 4. D 5. E A E D C B Clicker Question

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Example: You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 32 N m. Using the data in the drawing, determine the magnitude F of the force that you must exert on the wrench. θ τ sin rF = θ τ sin r F = N 149 ) 130 )(sin 28 . 0 ( 32 = = o
Example : What is the net torque produced by the forces F 1 and F 2 bout the rotational axis shown in the drawing? The forces are acting on a rigid rod, and the axis of rotation is perpendicular to the page. Include both magnitude and direction. x F 2 = 40.0 N F 1 = 10.0 N Axis 1.15 m 2.70 m 27 o From the figure, r 1 = 1.15 m, and r 2 = 2.70 m. θ 1 = 90 o θ 1 = 90 o θ 2 = 117 o θ 2 = 117 o F 1 produces a negative (cw) torque ( τ 1 ) F 2 produces a positive (ccw) torque ( τ 2 ) 1 2 τ τ τ - = net 1 1 1 1 sin θ τ F r = 2 2 2 2 sin θ τ F r = 1 1 1 2 2 2 sin sin θ θ τ F r F r net - = ) 90 )(sin 10 )( 15 . 1 ( ) 117 )(sin 40 )( 70 . 2 ( - = o m N 7 . 84 = Since the net torque is positive, the rod rotates ccw.

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9.2 Rigid Bodies in Equilibrium A rigid body is a fixed collection of masses (i.e. it’s not a point particle). Examples of rigid bodies: Every object is, in principle, a rigid body. In general, a rigid body could be moving linearly (translational motion) and it could also be spinning (rotational motion). Thus, for a rigid body to be in dynamic equilibrium, it must not be accelerating translationally or rotationally. Therefore, the following must be true: 0 = x F 0 = y F 0 = ext τ Translational Equilibrium Rotational Equilibrium
The second part just says that the sum of the external torques must be equal to zero. Thus, for rigid objects in equilibrium there are no linear accelerations, or angular accelerations. 9.3 Center of Gravity The weight of a rigid body can cause a torque on an object without any other external forces acting on the object.

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