Torque and Angular Acceleration

In summary, the moment of inertia of the pulley is 39.0 kg·m2 and the hanging mass exerts a force of 41.16 N. The net torque acting on the pulley is equal to the moment of inertia multiplied by the angular acceleration. However, there may be another component of the net torque and further calculations are needed to find it.
  • #1
r_swayze
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The pulley shown in the illustration has a radius of 2.70 m and a moment of inertia of 39.0 kg∙m2. The hanging mass is 4.20 kg and it exerts a force tangent to the edge of the pulley. What is the angular acceleration of the pulley?

All I have so far is the force exerted on the pulley by the block

mg = 4.2kg * 9.8m/s2 = 41.16N

which means it exerts a torque of r * F = 2.7m * 41.16N = 111.13Nm

I know net torque = moment of Inertia * angular acceleration, but I think I am missing another component of the net torque. What is that component and how do I find it?
 

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  • #2
damnit I'm working on this same problem right now... having the SAME issue ><
 

1. What is torque and how is it related to angular acceleration?

Torque is a measure of the force that causes an object to rotate about an axis. It is commonly represented by the symbol 'τ' and is calculated by multiplying the force applied to an object by the distance from the axis of rotation. Angular acceleration, on the other hand, is the rate of change of angular velocity. These two concepts are related through Newton's Second Law for rotational motion, which states that the net torque on an object is equal to the moment of inertia multiplied by the angular acceleration.

2. What is the unit of measurement for torque and angular acceleration?

The unit of measurement for torque is Newton-meters (N·m) in the SI system and foot-pounds (ft·lb) in the imperial system. Angular acceleration is measured in radians per second squared (rad/s²) in both systems.

3. How does the direction of torque and angular acceleration affect an object's motion?

The direction of torque and angular acceleration can determine the direction of an object's rotation. If the torque and angular acceleration are in the same direction, the object will rotate in the same direction. If they are in opposite directions, the object will rotate in the opposite direction. Additionally, the direction of torque and angular acceleration can also affect the axis of rotation of an object.

4. What factors affect the magnitude of torque?

The magnitude of torque depends on the force applied, the distance from the axis of rotation, and the angle between the force and the lever arm. The longer the lever arm and the greater the angle between the force and the lever arm, the larger the torque. Additionally, the direction of the force and the direction of the lever arm can also affect the magnitude of torque.

5. How is torque and angular acceleration used in real-life applications?

Torque and angular acceleration are used in many real-life applications, such as in the design and operation of machines, vehicles, and sports equipment. In vehicles, torque is used to accelerate and rotate the wheels, while angular acceleration is used to determine the turning radius. In sports, such as gymnastics and figure skating, torque and angular acceleration play a crucial role in executing rotations and twists. Furthermore, torque and angular acceleration are also important in the study of celestial mechanics, such as the rotation of planets and galaxies.

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