A rigid body is spinning with an angular speed of 60π radians per second (1800 rpm). The axis of rotation lies in the direction of the vector 2i + 2j -k. A small particle on the spinning body with mass of one kilogram passes through the point P with position vector r = xi + yj + zk measured in meters relative to the origin. The origin lies on the axis of rotation.
(i) Explain why the angular velocity (in units of radians per second) of the spinning rigid body is given by the vector 20π (2i + 2j - k).
(ii) What is the velocity (vector) of the particle as it passes through the point P?
(iii) Find an expression for the kinetic energy E of the particle, given in terms of its mass m and its speed v by E = 0.5mv2.