Solving Rotational Dynamics Problems with Torques & Acceleration

In summary, the conversation involves a problem with torques and acceleration where the participant believes they have the correct solution but is receiving an incorrect response. The problem involves a wheel of specific measurements and a weight attached to a cord, and the participant has set up equations using torque and tension to solve for the velocity and tension of the string. They mention using the equations T=m(g-a) and I*alpha=T*R to find the tension. They also mention using the equations F=mg, Torque=mgr, and Wf^2=Wi^2+2(alpha)(theta) to solve for the velocity. They are seeking suggestions for a solution to the problem.
  • #1
Electro
48
0
Hello,
I have a problem dealing with torques and acceleration. I am sure I solved it right but when submitting the answers, I get the response "Incorrect" :cry:

The problem:

A wheel of radius 2 m, mass 53 kg, and moment of inertia (3/4) (53 kg) (2m)^2 about the center of mass is mounted on a frictionless horizontal axle.
(g = 9.8). A light cord wrapped around the wheel supports an object of mass 106 kg. The weight is released from rest at the level of A and falls a distance h, past level B (AB=28 m). a) Find the velocity as it passes B b) Determine the tension of the string.

I set up everything.

Torque = I* alpha = T*R since alpha = a/R and we know I, conclusion is T=42*a

Then: T=m(g - a): putting T from above, I got a=7.0189189 m/s^2
To find V as the mass passes point B: Vf^2 = 2*a*28m ---> and v at B = 19.83 m/s. This was OK

For b) I used T=m(g-a), since I know a = 7.0189189m/s^2 , I substituted it at the equation and I got T= 294.79 N but this is not the right answer.

Maybe I can use I*alpha = T*R and from that get T because everything is known, but I am not sure. Any suggestions?
 
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  • #2
Can anyone help?
 
  • #3
For part a)
F=mg
Torque=mgr
mgr=I(alpha)
28=r(theta)
Wf^2=Wi^2+2(alpha)(theta)
Vf=r(Wf)

For part b)
a=R(alpha)
T=m(g-a)

Do these things help?
 

1. What is rotational dynamics?

Rotational dynamics is the branch of physics that deals with the motion of objects rotating around a fixed axis. It involves understanding the forces and torques acting on an object, as well as its acceleration and velocity.

2. What is torque?

Torque is a measure of the rotational force acting on an object. It is calculated by multiplying the force applied to an object by the distance from the point of rotation to where the force is applied. It is measured in units of Newton-meters (N*m).

3. How do you solve rotational dynamics problems?

To solve rotational dynamics problems, you need to first identify the forces and torques acting on the object. Then, you can use the equations of rotational motion, such as Newton's second law for rotational motion, to calculate the acceleration and velocity of the object.

4. What is the relationship between torque and acceleration?

There is a direct relationship between torque and acceleration. The greater the torque applied to an object, the greater its angular acceleration will be. This can be seen in the equation τ = Iα, where τ is torque, I is the moment of inertia, and α is angular acceleration.

5. What are some common applications of rotational dynamics?

Rotational dynamics has many practical applications, such as in the design and operation of machines, vehicles, and sports equipment. It is also used in understanding the motion of celestial bodies, such as planets and stars.

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