Need confirmation for this question please: A pulley with Radius of 90mm and a mass moment of inertia 0.28$kgm^2$ about its central axis is subjected to a torque of 50Nm about this axis. What is angular acceleration of the pulley?
Soo, I did this: $\tau=I_o \cdot alpha$, therefore angular acceleration alpha= 50/0.28= 178.6rad/s^2??
Isn’t that number too high for a pulley please? What am I missing?
Again your basic formula is just fine. $\tau=I_o \cdot \alpha$,. Therefore
$$ \alpha = \frac{\tau}{I_o}$$
The reason why you are getting such a high acceleration is due to the very high torque $\tau$ with respect to the reported mass moment of inertia and radius.
I would crosscheck the values regarding the mass moment of inertia because given the radius and the moment of inertia (by assuming that the pulley is a uniform disc), you can calculate the mass as:
$$m = \frac{2\cdot I_o}{R^2}\approx 70[kg]$$
A pulley with a diameter of 180[mm], weighing 80[kg] is not very likely. So its either a matter of some mistake in the mass moment of inertia or the mass.
