Find linear velocity v ⃗ \vec{v} v = ω ⃗ \vec{\omega} ω × r ⃗ \vec{r} r if r ⃗ \vec{r} r =(3 i ^ − 4 j ^ + k ^ \hat{i}-4\hat{j}+\hat{k} i ^ − 4 j ^ + k ^ ) and ω ⃗ \vec{\omega} ω =(5 i ^ − 6 j ^ + 6 k ^ \hat{i}-6\hat{j}+6\hat{k} i ^ − 6 j ^ + 6 k ^ ).
Physics · Rotational Motion · question based on pure rotation about fixed axis
AIPMT 1999 NEET

Question

Find linear velocity v ⃗ \vec{v} v = ω ⃗ \vec{\omega} ω × r ⃗ \vec{r} r if r ⃗ \vec{r} r =(3 i ^ − 4 j ^ + k ^ \hat{i}-4\hat{j}+\hat{k} i ^ − 4 j ^ + k ^ ) and ω ⃗ \vec{\omega} ω =(5 i ^ − 6 j ^ + 6 k ^ \hat{i}-6\hat{j}+6\hat{k} i ^ − 6 j ^ + 6 k ^ ).

Physics · Rotational Motion · question based on pure rotation about fixed axis

AIPMT 1999 NEET

G1 Physics · Accepted Answer

Step 1: Compute the determinant ω×r: i-component (-6)(1)-6(-4)=18; j-component 6(3)-5(1)=13; k-component 5(-4)-(-6)(3)=-2. Step 2: So v=18i+13j-2k. Final answer: B — 18i+13j-2k.

Find linear velocity v ⃗ \vec{v} v = ω ⃗ \vec{\omega} ω × r ⃗ \vec{r} r if r ⃗ \vec{r} r =(3 i ^ − 4 j ^ + k ^ \hat{i}-4\hat{j}+\hat{k} i ^ − 4 j ^ ​ + k ^ ) and ω ⃗ \vec{\omega} ω =(5 i ^ − 6 j ^ + 6 k ^ \hat{i}-6\hat{j}+6\hat{k} i ^ − 6 j ^ ​ + 6 k ^ ).

Find linear velocity v ⃗ \vec{v} v = ω ⃗ \vec{\omega} ω × r ⃗ \vec{r} r if r ⃗ \vec{r} r =(3 i ^ − 4 j ^ + k ^ \hat{i}-4\hat{j}+\hat{k} i ^ − 4 j ^ + k ^ ) and ω ⃗ \vec{\omega} ω =(5 i ^ − 6 j ^ + 6 k ^ \hat{i}-6\hat{j}+6\hat{k} i ^ − 6 j ^ + 6 k ^ ).