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

In summary, we have an object with a mass of 15.0 kg attached to a cord wrapped around a wheel with a radius of 9.0 cm. The object is accelerating down a frictionless incline at 2.00 m/s2. Using the formula t = Ia/r, we can determine the tension in the rope to be 58.46681 N. The moment of inertia of the wheel can then be calculated using the formula I = Fr^2/a and the angular speed of the wheel after 2.00 seconds of rotation can be determined.
  • #1
ace214
29
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
  • #2
I guess, the formula is t = Ia/r ... ain't it?
 
  • #3
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:

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

What is rotational inertia and why is it important?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to rotational motion. It is important because it determines how much torque is required to change the rotational motion of an object.

How do you calculate the rotational inertia of a wheel?

The rotational inertia of a wheel can be calculated using the formula I = 1/2 * MR^2, where I is the moment of inertia, M is the mass of the wheel, and R is the radius of the wheel.

What is a frictionless incline and how does it affect the calculation of rotational inertia?

A frictionless incline is an inclined surface with no friction present. This means that there is no force acting against the motion of the object, making it easier to calculate the rotational inertia as there is no need to account for friction in the calculations.

Can the rotational inertia of an object change?

Yes, the rotational inertia of an object can change depending on its mass distribution and shape. For example, a solid disk has a different rotational inertia than a hollow disk with the same mass and radius.

How does the mass distribution of an object affect its rotational inertia?

The mass distribution of an object affects its rotational inertia as it determines how the mass is distributed around the axis of rotation. Objects with more mass concentrated towards the axis of rotation have a smaller moment of inertia than objects with mass distributed farther from the axis.

Similar threads

B Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
    • Mechanics
Replies
2
Views
146
Question on Moment of Inertia/Rotational Inertia
    • Introductory Physics Homework Help
Replies
4
Views
2K
How Does the Rotational Inertia Affect Rolling Motion on an Inclined Plane?
    • Introductory Physics Homework Help
Replies
3
Views
2K
Calculating Tension, Moment of Inertia, and Angular Speed in a Rotating System
    • Introductory Physics Homework Help
Replies
5
Views
2K
Calculation of torque to stop a wheel.
    • Introductory Physics Homework Help
Replies
4
Views
5K
Moment of inertia of a wheel: linear to angular motion
    • Introductory Physics Homework Help
Replies
6
Views
2K
Rotational Motion Two Questions
    • Introductory Physics Homework Help
Replies
12
Views
4K
Calculating tangential acceleration of rotating object
    • Introductory Physics Homework Help
Replies
2
Views
2K
Calculating the Force on a Bicycle Wheel
    • Introductory Physics Homework Help
Replies
2
Views
3K
Angular Acceleration and torque problem
    • Introductory Physics Homework Help
Replies
22
Views
3K

Hot Threads

Recent Insights

Back
Top