Math Problem Statement
A centripetal
acceleration addict rides in uniform circular motion with period T
2 . 0 s and radius r
2 . 6 0 m . At t 1 his acceleration is vec ( a )
( 6 . 8 0 m s 2 ) h a t ( i ) + (
3 . 8 0 m s 2 ) h a t ( j ) . At that instant, what are the values of ( a ) v e c ( v ) * v e c ( a ) and ( b ) v e c ( r ) × vec ( a )
? ( a ) Number Units ( b ) Number i hat ( i ) i hat ( j ) + i hat ( k ) Units
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Kinematics
Uniform Circular Motion
Formulas
Dot product formula: vec(v) ⋅ vec(a) = |v||a|cos(θ)
Cross product formula: vec(r) × vec(a) = |r||a|sin(θ) hat(k)
Centripetal acceleration: a_c = v^2/r
Theorems
Properties of dot product: orthogonal vectors yield zero
Properties of cross product: direction follows the right-hand rule
Suitable Grade Level
Grades 11-12
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