Label as true or false. Explain your answer or give a counterexample. [Hint - it may be useful to think about circular motion about the origin.]

Question

Quizplus · Accepted Answer

Note that 11eaa948_cda7_6302_84bc_c7d3e03918f2_TB2342_11 is the rate of change of the length of the vector 11eaa948_cda7_6303_84bc_8bbd57fa8174_TB2342_11 and may be zero even if the terminal point of 11eaa948_cda7_6304_84bc_4b451374c046_TB2342_11 is translating through space (this is precisely the case for circular motion about the origin). On the other hand, 11eaa948_cda7_8a15_84bc_8da688826080_TB2342_11 is the magnitude of the vector 11eaa948_cda7_8a16_84bc_c971ef367f6e_TB2342_11 and is zero only if 11eaa948_cda7_8a17_84bc_492bd8daabcf_TB2342_11 (that is, if the vector 11eaa948_cda7_8a18_84bc_1f80c2f4965a_TB2342_11 is stationary at time t). For circular motion about the origin, then, 11eaa948_cda7_8a19_84bc_3b75827570d3_TB2342_11 whereas 11eaa948_cda7_8a1a_84bc_25fd951fcfa5_TB2342_11 . Therefore, 11eaa948_cda7_8a1b_84bc_85b742f323e1_TB2342_11 .

Label as True or False