A particle of mass m is moving in time t on a trajectory given by, r → = 10 α t 2 i ^ + 5 β t - 5 j ^ where α and β are dimensional constants. The angular momentum of the particle becomes the same as it was for t = 0 at time t = _____ seconds.

Question

A particle of mass m is moving in time t on a trajectory given by, r &#8594; = 10 &#945; t 2 i ^ + 5 &#946; t - 5 j ^ where &#945; and &#946; are dimensional constants. The angular momentum of the particle becomes the same as it was for t = 0 at time t = _____ seconds.

Aicharya · Accepted Answer

r &#8594; = 10 &#945; t 2 i ^ + 5 &#946; t - 5 j ^ v &#8594; = 20 &#945; + i ^ + 5 &#946; j ^ L &#8594; = m r &#8594; &#215; v &#8594; = m 10 &#945; t 2 i ^ + 5 &#946; t - 5 j ^ &#215; 20 &#945; i ^ + 5 &#946; j ^ L &#8594; = m 50 &#945; &#946; t 2 k ^ - 100 &#945; &#946; t 2 - 5 t k ^ At t = 0 , &#160; L &#8594; = 0 &#8594; 50 &#945; &#946; t 2 - 100 &#945; &#946; t 2 - 5 t = 0 t - 2 t - 5 = 0 t = 10 &#160; sec

A particle of mass m is moving in time t on a trajectory given by, r → = 10 α t 2 i ^ + 5 β…

Solution

A particle of mass m is moving in time t on a trajectory given by, r &#8594; = 10 &#945; t 2 i ^ + 5 &#946;…

Solution

A particle of mass m is moving in time t on a trajectory given by, r → = 10 α t 2 i ^ + 5 β…