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# lecture3 - Torque and Rotational Dynamics I mr 2 Moment of...

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Torque and Rotational  Dynamics 2 I mr ≡ Σ Parallel Axis Theorem Moment of Inertia definition

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Rotational Kinetic Energy          KE r = ½Iω 2   Translational Kinetic Energy KE t = ½mv 2 Work Energy Principle
6. I 0 solid sphere = 2 / 5 mr 2 Lecture Quiz Q1

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Lecture Quiz Q2   KE r = ½Iω 2    I 0 = 1 / 12 mL 2 I = I 0 + mL 2 A rod (mass 2.5 kg and length of 2 m) is at rest in horizontal position. The rod falls down without a friction. What would be the rod angular velocity when it was in vertical position? A 3.1 rad / s B 2.5 rad / s C 1.4 rad / s D 3.8 rad / s E 4.7 rad / s
A 2.5 kg rod of length 2 m with a small mass 0.5 kg attached at the center rotates about one end with rotational velocity ϖ = 3 rad / s . What would be the angular velocity if the mass was moved to the far end of the rod and the total energy (rotatioal) remained the same?   KE r = ½Iω 2    I 0 = 1 / 12 mL 2 I = I 0 + mL 2 2 I mr ≡ Σ Lecture Quiz Q3 A 1.2 rad / s B 1.5 rad / s C 1.8 rad / s D 2.1 rad / s E 2.5 rad / s

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6. I 0 solid sphere = 2 / 5 mr 2 Lecture Quiz Q1 I = I 0 +md 2 = 2 / 5 mr 2 + m*r 2 = 7 / 5 mr 2
Lecture Quiz Q2   KE r = ½Iω 2    I 0 = 1 / 12 mL 2 I = I 0 + mL 2 A rod (mass 2.5 kg and length of 2 m) is at rest in horizontal position. The rod falls down without a friction. What would be the rod angular velocity when it was in vertical position? I 1 3 m L 2 = K i 0 = h L 2 = U i m g h = E Total K i U i + = E 24.5 = U f 0 = K f E = ϖ 2 K f I = ϖ 3.834 =

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A 2.5 kg rod of length 2 m with a small mass 0.5 kg attached at the center rotates about one end with rotational velocity ϖ = 3 rad / s . What would be the angular velocity if the mass was moved to the far end of the rod and the total energy (rotatioal) remained the same?   KE r = ½Iω 2    I 0 = 1 / 12 mL 2 I = I 0 + mL 2 2 I mr ≡ Σ Lecture Quiz Q3 I i 1 3 M L 2 m L 2 2 + = K i 1 2 I i ϖ 2 = I i 3.833 = K i 17.25 = I f 1 3 M L 2 m L 2 + = I f 5.333 = ϖ 2 K i I f = ϖ 2.543 =
Force vs. Torque Forces cause linear accelerations Torques cause angular accelerations Force and torque are related

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Torque The  door  is free to rotate about an axis through O There are three factors that determine the
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## This note was uploaded on 02/22/2009 for the course PHYS 106 taught by Professor Opyt during the Spring '08 term at NJIT.

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lecture3 - Torque and Rotational Dynamics I mr 2 Moment of...

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