Question

A centripetal-acceleration addict rides in uniform circular motion with radius

r = 3.00 m. At one instant his acceleration is ⃗a =(6.00 m/s2
)ˆı+(4.00 m/s2

)ˆȷ.

At that instant, what are the values of (a) ⃗v · ⃗a (b) ⃗r × ⃗a?

Answer 1

Acceleration = $6\hat{i} + 4\hat{j}$

Therefore, Centripetal acceleration  = 6

∴ 6 = v²/r

⇒ v² = 6 × 3

⇒ v = √18 m/s.

or v = √18 j^

∴ (a).         $\vector{v}. \vector{a}$ = √18 j^ . 4 j^

  = 4 × 3√2 = 12√2

(b).   $\vector{r} x \vector{a}$ = -3i x (6i + 4j)

= -12 k

Magnitude = 12

Hope it helps.

Answer 2

Answer:

Therefore, Centripetal acceleration  = 6

∴ 6 = v²/r

⇒ v² = 6 × 3

⇒ v = √18 m/s.

or v = √18 j^

∴ (a).         = √18 j^ . 4 j^

  = 4 × 3√2 = 12√2

(b).   = -3i x (6i + 4j)

= -12 k

Magnitude = 12