Simple concept help: Pulley and Net Torque

In summary, for a ball of radius .11m and mass .444kg mounted on a frictionless axle with a massless cord wrapped around it supporting an object of mass .02kg, the angular acceleration of the wheel is .72 rad/s^2, the linear acceleration of the object is .72 m/s^2, and the tension in the cord is 0.2975 N. Be mindful of the signage for accurate calculations.
  • #1
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Homework Statement


A ball (hollow sphere) of radius .11m and mass .444kg is mounted on a frictionless axle. A massless cord is wrapped around the ball supporting an object of mass .02kg. Find the angular acceleration of the wheel, linear acceleration of the object and tension in the cord.


Homework Equations





The Attempt at a Solution


[tex]\Sigma[/tex]F=Fg+T=m*a
-.2+T=.02a

[tex]\Sigma[/tex][tex]\tau[/tex]=F*r=I*[tex]\alpha[/tex]
-T*.11=(.0036*a)/.11
T = -.2975*a

-.2 + .2975*a = .02*a
-.2 = -.2775a
.72 = a

That's what I tried, but it's wrong.
Can anyone help?
 

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  • #2
john562 said:

Homework Statement


A ball (hollow sphere) of radius .11m and mass .444kg is mounted on a frictionless axle. A massless cord is wrapped around the ball supporting an object of mass .02kg. Find the angular acceleration of the wheel, linear acceleration of the object and tension in the cord.


Homework Equations





The Attempt at a Solution


[tex]\Sigma[/tex]F=Fg+T=m*a
-.2+T=.02a
0.2 -T = .02a
[tex]\Sigma[/tex][tex]\tau[/tex]=F*r=I*[tex]\alpha[/tex]
-T*.11=(.0036*a)/.11
T*.11 = .0036a/.11
T = -.2975*a
T = .2975a
-.2 + .2975*a = .02*a
-.2 = -.2775a
.72 = a

That's what I tried, but it's wrong.
Can anyone help?
You must watch your signage. The acceleration is downwards. Choose the downward and clockwise directions as positive, for compatability and simplicity.
 

1. What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or belt that runs along the groove. It is used to change the direction of a force or to lift an object by pulling down on one end of the rope while the object is attached to the other end.

2. How does a pulley work?

A pulley works by distributing the weight of an object evenly between multiple ropes or cables. When one end of the rope is pulled, the other end also moves, causing the pulley to rotate. This reduces the amount of force needed to lift the object, making it easier to move.

3. What is net torque?

Net torque refers to the overall rotational force acting on an object. It takes into account the individual torques from all the forces acting on the object and determines whether the object will rotate clockwise or counterclockwise.

4. How is net torque calculated?

Net torque is calculated by multiplying the force applied to the object by the distance from the pivot point (or the point where the object rotates). This can be represented by the equation: Net Torque = Force x Distance.

5. How does a pulley affect net torque?

A pulley can affect net torque by changing the direction of the force and/or by changing the distance from the pivot point. For example, if a pulley is used to lift an object, it may decrease the distance from the pivot point, resulting in a higher net torque and making it easier to lift the object.

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