the position vectors of the head and tail of radius vectors are 2i+j+k and 2i-3j+k. the linear momomentum is 2i+3j+k. the angular momentum is
4i-8k
To find the angular momentum, we need to find the cross product of the position vector and the linear momentum.
The formula for the cross product of two vectors A and B is given by:
A × B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k
Given that the position vector of the head of the radius vector is 2i + j + k and the linear momentum is 2i + 3j + k, we can calculate the cross product:
(2 * (2) - (1) * (3))i + ((1) * (1) - (2) * (2))j + ((2) * (3) - (2) * (1))k
= 4i - 3j + 4k
So, the angular momentum is 4i - 3j + 4k.
To find the angular momentum, we need to calculate the cross product of the position vector and the linear momentum.
Angular momentum = r x p
Given:
Position vector of the head of the radius vector, r1 = 2i + j + k
Position vector of the tail of the radius vector, r2 = 2i - 3j + k
Linear momentum, p = 2i + 3j + k
First, let's find the vector representing the radius vector, r.
r = r1 - r2
= (2i + j + k) - (2i - 3j + k)
= 2i + j + k - 2i + 3j - k
= i + 4j
Now, we can calculate the cross product of the radius vector and the linear momentum:
Angular momentum = r x p
= (i + 4j) x (2i + 3j + k)
= (1 * (3j) - 4j * (k)) i + (1 * (2i) - i * (k)) j + ((i * (4j) - (1 * (2i))) k)
= -4j - 2i - 2k
Therefore, the angular momentum is -2i - 4j - 2k.