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.

Step-by-step solution

r → = 10 α t 2 i ^ + 5 β t - 5 j ^ v → = 20 α + i ^ + 5 β j ^ L → = m r → × v → = m 10 α t 2 i ^ + 5 β t - 5 j ^ × 20 α i ^ + 5 β j ^ L → = m 50 α β t 2 k ^ - 100 α β t 2 - 5 t k ^ At t = 0 ,   L → = 0 → 50 α β t 2 - 100 α β t 2 - 5 t = 0 t - 2 t - 5 = 0 t = 10   sec