The radius vector `vec r=2i+5k` and the angular velocity of a particle is `vec w=3i-4k` Then the linear velocity of the particle is

The position vector of a particle is vec( r) = a cos omega t i + a sin omega t j , the velocity of the particle is

The angular velocity of a particle is vec(w) = 4hati + hatj - 2hatk about the origin. If the position vector of the particle is 2hati + 3hatj - 3hatk , then its linear velocity is

In nonuniform circular motion, the linear acceleration vec a , the angular acceleration, vec alpha , the angular velocity vec v the radius vector vec r and the angular velocity vec omega at any instant are related by the vector equation,

If angular velocity of a particle having position vector vec r = (2hati - 2hatj + 2hatk)m about the origin is vec w = (2hati - 2hatj - hatk)rad/s then magnitude of linear velocity of the particle will be

The position of a particle is given by vec(r) = 3that(i) - 4t^(2)hat(j) + 5hat(k). Then the magnitude of the velocity of the particle at t = 2 s is

The linear velocity of a rotating body is given by vec(v)= vec(omega)xxvec(r ) , where vec(omega) is the angular velocity and vec(r ) is the radius vector. The angular velocity of a body is vec(omega)= hat(i)-2hat(j)+2hat(k) and the radius vector vec(r )= 4hat(j)-3hat(k) , then |vec(v)| is

The linear velocity of a rotating body is given by vec(v)=vec(omega)xxvec(r) , where vec(omega) is the angular velocity and vec(r) is the radius vector. The angular velocity of a body is vec(omega)=hat(i)-2hat(j)+2hat(k) and the radius vector vec(r)=4hat(j)-3hat(k) , then |vec(v)| is-

The angular velocity of a rotating body is vec omega = 4 hat i + hat j - 2 hat k . The linear velocity of the body whose position vector 2hati + 3 hat j - 3 hat k is

A particle moves along a circle of radius R =1m so that its radius vector vecr relative to a point on its circumference rotates with the constant angular velocity omega=2rad//s . The linear speed of the particle is

The linear velocity of a rotating body is given by v =omega xx r , where omega is the angular velocity and r is the radius vector. The angular velocity of a body omega=hati-2hatj+2hatk and their radius vector r=4hatj-3hatk, |v| is -