Calculate Rotational Inertia of Wheel | 15kg Object on Frictionless Incline

AI Thread Summary
A 15.0-kg object on a frictionless incline is connected to a wheel with a radius of 9.0 cm, and its acceleration is measured at 2.00 m/s². The tension in the rope is calculated to be approximately 58.47 N. The discussion revolves around determining the moment of inertia of the wheel, with participants struggling to apply the correct formulas. The correct formula for calculating the moment of inertia is confirmed as I = Fr²/a. This exchange highlights the importance of using the right equations in rotational dynamics.
ace214
Messages
28
Reaction score
0
A 15.0-kg object is attached to a cord that is wrapped around a wheel of radius r = 9.0 cm (Fig. P8.60). The acceleration of the object down the frictionless incline is measured to be 2.00 m/s2. Assume the axle of the wheel to be frictionless.

p8-60alt.gif


(a) Determine the tension in the rope.
58.46681 N
(b) Determine the moment of inertia of the wheel.
kg·m2
(c) Determine the angular speed of the wheel 2.00 s after it begins rotating, starting from rest.
rad/s
===================================
The tension is correct. I'm stuck on the inertia. I'll use 't' for torque and 'T' for the tension.

t=Iar => I = t/ar = Fr/ar = T/a but this doesn't work. I also tried using the force of gravity and the sigma force in the above equation and none of them are correct.Due tomorrow morning at 8:30 AM EST... :-(
 
Last edited:
Physics news on Phys.org
I guess, the formula is t = Ia/r ... ain't it?
 
saket said:
I guess, the formula is t = Ia/r ... ain't it?
... Crap

Yeah that did it. Thanks.

So for anyone searching the formula becomes
I = Fr^2/a
 
Last edited:

Thread 'Errors and significant figures'

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...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

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...
View full post »
Thread 'A cylinder connected to a hanging mass'

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...
View full post »

Similar threads

Question on Moment of Inertia/Rotational Inertia
Replies
4
Views
2K
How Does the Rotational Inertia Affect Rolling Motion on an Inclined Plane?
Replies
3
Views
2K
B Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
Replies
2
Views
1K
Rotational Motion Two Questions
Replies
12
Views
4K
Calculating Tension, Moment of Inertia, and Angular Speed in a Rotating System
Replies
5
Views
2K
Calculation of torque to stop a wheel.
Replies
4
Views
6K
Moment of inertia of a wheel: linear to angular motion
Replies
6
Views
2K
Inertia block on inclined surface problem? help with solution?
Replies
5
Views
2K
How Do You Calculate the Moment of Inertia for a Rotating Wheel?
Replies
3
Views
2K
Calculating the Force on a Bicycle Wheel
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top