Angular acceleration given force, moment arm and inertia?

In summary, angular acceleration is the rate of change of an object's angular velocity and is measured in radians per second squared. It is directly proportional to the net torque (force) applied to the object, with a greater force resulting in a greater angular acceleration. The moment arm, which is the distance from the axis of rotation to the point of force application, determines the torque and thus the angular acceleration. Inertia, or an object's resistance to changes in motion, also plays a role in angular acceleration by requiring more force to achieve the same acceleration in objects with greater inertia. To calculate angular acceleration, use the formula α = τ/I, where α is the angular acceleration, τ is the net torque, and I is the moment of inertia
  • #1
joema
106
3

Homework Statement



Find angular acceleration in deg/sec^2 given the following factors:

- Total mass: 4889 kg
- Moment of inertia: 4620 kg*m^2
- Moment arm length from center of mass: 1.5 meters
- Force on moment arm tangent to mass: 1779 Newtons

Homework Equations



torque = force * moment arm length
torque = 1779 Newtons * 1.5 meters
torque = 2668.5 Newton-meters

angular acceleration = torque / moment of inertia

The Attempt at a Solution



angular acceleration = 2668.5 N-m / 4620 kg*m^2

angular acceleration = 0.576 radians/sec^2 = 33.05 degrees/sec^2

Is this right?
 
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  • #2
Looks good, except for significant digits.
 
  • #3
Should be 33, yes? i.e. 2 sig figs
 
  • #4
Yep.
 
  • #5


I would say that your solution appears to be correct based on the given information and equations. However, it is important to note that without units, the value for angular acceleration is incomplete. Also, it would be beneficial to explain the significance or meaning of the calculated angular acceleration in the context of the problem. Additionally, it is always a good practice to double check your calculations and units to ensure accuracy.
 

Related to Angular acceleration given force, moment arm and inertia?

1. What is angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is measured in radians per second squared (rad/s^2).

2. How is angular acceleration related to force?

Angular acceleration is directly proportional to the net torque (force) applied to an object. The greater the force, the greater the angular acceleration.

3. What is the moment arm in relation to angular acceleration?

The moment arm is the perpendicular distance from the axis of rotation to the point where the force is applied. It determines the torque, and therefore, the angular acceleration of an object.

4. How does inertia affect angular acceleration?

Inertia, which is the resistance of an object to changes in its state of motion, affects angular acceleration by determining how much force is needed to change the object's angular velocity. Objects with greater inertia require more force to achieve the same angular acceleration as objects with lower inertia.

5. How do you calculate angular acceleration given force, moment arm, and inertia?

The formula for calculating angular acceleration is α = τ/I, where α is the angular acceleration in radians per second squared, τ is the net torque (force x moment arm), and I is the moment of inertia of the object. Plug in the known values and solve for α.

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