Need help with some physics questions!?

Posted on 2015-11-28 07:59:00 in Physics by ELISA

Did more than half of the homework, but couldn't figure these ones out, please help! Thanks!

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity v in the negative x direction, and a second piece, also of mass m, moves with the same velocity in the negative y direction. The third piece has mass 3m. Just after the explosion, (a) what is the magnitude of the velocity of the third piece in terms of the given variables? (b) What is the direction of its motion (as an angle relative to the positive x axis)?

A uniform cylinder of radius R and mass M is mounted so as to rotate freely about a horizontal axis that is parallel to, and a distance h from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position? State your answers in terms of the given variables, using g when appropriate.

At time t = 0, a particle of mass m has position vector r=4i-2j relative to the origin, in meters. For t ? 0, its velocity is given by v=-6t^2i+4j With v in m/s and t in seconds. Find expressions of the z component of (a) the particle's angular momentum and (b) the torque acting on the particle at time t.

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