PHY2048 Physics 1, Chapters 6 to 10 Equations Study Guide - Chapter 6 Work and Kinetic Energy Equations = = cos = = 1 2 2 = = 2 = = 1 1 1 2 2 2 2 1 =

# PHY2048 Physics 1, Chapters 6 to 10 Equations Study Guide -...

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Unformatted text preview: Chapter 6: Work and Kinetic Energy Equations : = = ( cos ) ( , ℎ ) : = ⃗ ∙ ⃗ ( , ℎ ) : = 1 2 ( ) 2 − ℎ: = − = ∆ 2 : = ∫ = 1 1 1 2 − 2 2 2 1 = 2 2 = 1 2 1 2 − 2 2 ′ : = ( ℎ ) 2 ℎ: = ∫ 2 cos ∅ = ∫ 1 2 ∥ = ∫ 1 ⃗ ∙ ⃗⃗⃗⃗ 1 ∆ ∆ = = ∆ ∆ ∆ : = lim = ∆→0 ∆ : = ℎℎ ⃗ : = ⃗ ∙ ⃗ Chapter 7: Potential Energy and Energy Conservation Equations : = = ( − ) = − = , − , = −∆ : = ℎ : + , = + , ℎ ℎ ℎ : + , + ℎ 1 1 2 + = 2 + ( ) 2 2 1 1 = + , 2 + + ℎ = 2 + 2 2 1 2 2 1 1 : = 2 − 2 = , − , = −∆ 2 2 1 1 1 1 − ℎ (): + , = + , 2 + 2 = 2 + 2 2 2 2 2 ( ): + , + , + ℎ = + , + , : = ( ): + + ℎ = + : ∆ + ∆ + ∆ = 0 () ̂) , ℎ : () = − ( ̂ + ̂ + , : () = − Chapter 8: Momentum, Impulse, and Collisions Equations : ⃗ = (: . ∴ ⃗⃗⃗⃗⃗ = ⃗ ⃗⃗⃗⃗⃗, ⃗⃗⃗⃗⃗ = ⃗⃗⃗⃗⃗, ⃗⃗⃗⃗ = ⃗⃗⃗⃗ : ⃗⃗ = ⃗ + ⃗ + ⃗ + ⋯ = ⃗⃗⃗⃗ + ⃗⃗⃗⃗ + ⃗⃗⃗⃗ + ⋯ ( ) ′ : ∑ = Conservation of Momentum: The total momentum of a system is constant whenever the vector sum of the external forces on the system is zero. In particular, the total momentum of an isolated system is constant. 2 : ⃗ = ⃗ ( − ) = ⃗ ∆ : = ∫ ∑ 1 ℎ ( − ℎ): ⃗ = ⃗⃗⃗⃗2 − ⃗⃗⃗1 : = ∆ = , − , = , − , = ∆ = , − , = , − , : ⃗ = ⃗⃗⃗⃗⃗⃗⃗⃗⃗( − ) Inelastic Collisions: : ( ,, ) + ( ,, ) = ( + )( , ) : , = : ( ) − ,, = − Elastic Collisions: : 1 1 1 1 2 + 2 = 2 + 2 2 , 2 , 2 , 2 , : , + , = , + , : 1 1 1 2 = 2 + 2 ( , ) 2 , 2 , 2 , : , = , + , ( , ) : , = − 2 ( , ) , = ( ) + + , : , − , = , : = ⃗ , − ⃗ , = −( , − ⃗ , ) ⃗ + + + ⋯ ∑ = ∑ + + +⋯ : = : ⃗ = + + +⋯ + + + ⋯ = + + +⋯ + + +⋯ ⃗⃗⃗⃗⃗ + ⃗⃗⃗⃗⃗ + ⃗⃗⃗⃗⃗ + ⋯ + + +⋯ : = + + + ⋯ = ⃗⃗ ⃗ : ∑ ⃗ = ( ) ⃗⃗⃗⃗⃗⃗⃗⃗ : ∑ ⃗ = ⃗ ( ) Chapter 9: Rotation of Rigid Bodies Equations ℎ: = 2 = 1 = / 60 ∆ : = lim = ∆→0 ∆ 2 − 1 ∆ : = = 2 − 1 ∆ 1 = 2 1 ∆ = ∆→0 ∆ : = lim : = : = 2 − 1 ∆ = 2 − 1 ∆ + + = 2 −0 Constant acceleration ONLY equations of rotational motion : = + ℎ : = + + 1 2 2 : 2 = 2 + 2( − ) 1 : − = ( + ) 2 : = : = ( ) : = 2 = 2 : , = ( ) = ( 2 ) ℎ : , = , : | = = √2 + 2 ⃗| : = 2 + 2 + 2 + ⋯ = ∑ 2 : = ( 2 + 2 + 2 + ⋯ ) : = 1 2 ( ) 2 Chapter 10: Dynamics of Rotational Motion : = = ( sin ) = (; ) : = × : ∑ = , + + ⋯ = ( 2 + 2 + ⋯ ) : = 1 1 2 + 2 ( ℎ ℎ ) 2 2 : = ℎ : = : ∑ ⃗⃗⃗⃗⃗⃗⃗ = ∑ = 2 : = ∫ 1 : = (2 − 1 ) = ∆ 2 : = ∫ 1 = 1 2 1 2 − 2 2 2 1 : = : ⃗ = = ( 2 + 2 + 2 + ⋯ ) ⃗ ℎ : ∑ = = sin = ⃗ ( ) Conservation of angular momentum: When the sum of the torques of all the external forces acting on a system is zero, the total angular momentum of the system is constant (conserved). : ⃗ =0 = ...
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