What is the Initial Angular Acceleration of a Disk Released from Rest?

AI Thread Summary
The initial angular acceleration of a disk released from rest can be calculated using the torque equation, Torque = Iα. The weight of the disk is determined to be 49 N, and the radius used for torque calculation is 0.3 m, resulting in a torque of 14.7 N·m. The moment of inertia must be adjusted using the Parallel Axis theorem since the axis of rotation is not through the center of mass. The correct moment of inertia is calculated as I = I_{CM} + MD^2, where I_{CM} is the moment of inertia for a solid disk. This adjustment leads to the accurate calculation of angular acceleration.
klm
Messages
165
Reaction score
0
A 5.0 kg, 60-cm-diameter disk rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle, then released.

What is the cylinder's initial angular acceleration?

7x2f413.jpg


ok so this is what i think i should do:

Torque= I \alpha

and i need to find the F(weight)= mg = (5)(9.8) = 49 N
radius = .5(.6)= .3
Torque= Fd = 49(.3) = 14.7
14.7 = I \alpha
this is the part which i am not sure on, does I = .5 m r^2 = .5(5)(.3^2) = .225
14.7 .225 \alpha
\alpha = 65.33
but this answer is incorrect, and i do not know where i am making the mistake.
 
Physics news on Phys.org
please can someone help
 
Try using the Parallel Axis theorem to find the moment of inertia. This is needed because the axis of rotation is not through the centre of mass of the disk.

I = I_{CM} + MD^2

where I_{CM} is the moment of inertia for a solid disk, M is the mass of the disk and D is the distance from the centre of mass to the new axis.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top