does the tangential acceleration depend on the change in the angular velocity?
Answer Hello Robert, Yes. Tangential means perpendicular to a radius. Let’s talk about velocity first. Velocity in the tangential direction of a particle is directly related to the angular velocity. Let the angular velocity be 1 rev/sec. In one second the particle makes one revolution, so it travels one circumference = 2*pi*r. So its tangential velocity is 2*pi*r/sec. OK, now let’s say the object is under a torque from a hanging mass. It was being held, but it is now released and accelerates at 1 rev/sec^2. At the end of the first second the object has an instantaneous angular velocity of 1 rev/sec and the particle’s instantaneous tangential velocity is 2*pi*r/sec. One second later the object has an instantaneous angular velocity of 2 rev/sec and the particle’s instantaneous tangential velocity is 4*pi*r/sec. Calculate the tangential acceleration using the interval from the end of second 1 to the end of second 2: a = delta v/delta t = (2*pi*r/sec)/1 sec = 2*pi*r/sec^2. Watch the units:
