A block moves outward along the slot in the platform with a speed of r =(4t)m/s, where t is in seconds. The platform rotates at a constant rate of 6 rad/s. If the block starts from rest at the center, determine the magnitudes of its velocity and acceleration when t = 1 s.

Question

A block moves outward along the slot in the platform with a speed of \dot { r } =(4t)m/s, where t is in seconds. The platform rotates at a constant rate of 6 rad/s. If the block starts from rest at the center, determine the magnitudes of its velocity and acceleration when t = 1 s.

Accepted Answer

[latex]\dot { r } =4t{ | }_{ t=1 }=4\quad \quad \ddot { r } =4\ \dot { heta } =6\quad \quad \ddot { heta } =0\ \int _{ 0 }^{ 1 }{ dr } =\int _{ 0 }^{ 1 }{ 4t } dt\ r={ 2t }^{ 2 }{ ] }_{ 0 }^{ 1 }=2m\ v=\sqrt { { (\dot { r } ) }^{ 2 }+{ (r\dot { heta } ) }^{ 2 } } =\sqrt { { (4) }^{ 2 }+{ [2(6)] }^{ 2 } } =12.6m/s\ a=\sqrt { { (\ddot { r } -r\dot { { heta }^{ 2 }) } }^{ 2 }+{ (r\ddot { heta } +2\dot { r } \dot { heta ) } }^{ 2 }= } \sqrt { { [4-2({ 6) }^{ 2 }] }^{ 2 }+{ [0+2(4)(6)] }^{ 2 } } =83.2m/{ s }^{ 2 }[/latex]

Question : A block moves outward along the slot in the platform with a ...

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