How Do You Calculate Angular Acceleration of a Cylinder?

[sheri1987]

Homework Statement

M, a solid cylinder (M=1.67 kg, R=0.137 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.670 kg mass, i.e., F = 6.573 N. Calculate the angular acceleration of the cylinder.

Homework Equations

F*R ?
ang accel. = alpha*R

The Attempt at a Solution

I multiplied Force*Radius, cause someone told me to start with that, but I'm not sure what to do next?

 

[rl.bhat]

F*R = Torque = I*alpha. where I is the moment of inertia of the solid cylinder=MR^2/2

 

[ogb p]

I would approach this problem by first defining the variables and equations involved. The cylinder is attached to a wall, meaning it is free to rotate around a fixed point. The given information includes the mass of the cylinder (M), its radius (R), and the force acting on it (F).

To calculate the angular acceleration of the cylinder, we can use the equation alpha = torque/I, where torque is the product of force and distance from the pivot point (in this case, the radius), and I is the moment of inertia of the cylinder.

Using the given information, we can calculate the torque as F*R. To find the moment of inertia, we can use the formula I = 1/2*M*R^2 for a solid cylinder rotating around its central axis. Plugging in the values, we get I = 1/2*1.67 kg*(0.137 m)^2 = 0.012 kg*m^2.

Now we can plug these values into the equation for angular acceleration: alpha = (F*R)/I. Substituting in the known values, we get alpha = (6.573 N * 0.137 m)/0.012 kg*m^2 = 75.96 rad/s^2.

Therefore, the angular acceleration of the cylinder is 75.96 rad/s^2.