angular acceleration Watch
A winding drum with a moment of inertia of 24kgm2 and winding radius of 0.6m is used to accelerate a loaded hoist of mass 850kg at a rate of 0.8ms2 by means of cable. the total frictional resistance of the system can be considered as a torque of 88Nm acting about the drum shaft.
i need to calculate:
a) tension in kn required in cable.
b) angular acceleration in rad/s at the winding drum shaft.
c) accelerating torque in Nm required at the winding drum shaft to accelerate the system.
d) the total driving torque in Nm required at the winding drum shaft to produce the required motion of the whole system.
ive managed question (a) but stuck on the rest, any help would be appreciated.
b) you should have a simple means of changing 0.8ms-2 to rad s-2 - assuming the cable is inextensible then the change in linear speed of the winding circle must be the same as the acceleration of the mass upwards
c) Now that you have the angular acceleration you should be able to work out the torque required to produce this
d) Finally, the driving torque needs to both provide the torgue you calculate in (c) AND cancel the effect of the frictional torque.
If it helps, I often remember first the linear equations and then convert them to their angular equivalents.
ie for (c) F = ma would become Torque = I x angular acc
and of course, for (b) we know ω = v/r and similarly α = a/r
Hope this helps.