Initial Acceleration of a Center of Mass

In summary, a uniform rod of length 1.25 m is released from rest from an angle θ = 23.0° above the horizontal. To find the magnitude of the initial acceleration of the rod's center of mass, one can use the fact that the center of mass lies at 1/2 * L and that gravity grips the rod here. Using a simple geometric rule, the force perpendicular to the rod can be found, leading to the initial acceleration. Alternatively, the torque exerted by gravity can be calculated and related to the linear acceleration of the center of mass using the formula \alpha D = a.
  • #1
mparsons06
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Homework Statement



A uniform rod of length 1.25 m is attached to a frictionless pivot at one end. It is released from rest from an angle θ = 23.0° above the horizontal.

PivotRod.gif


Find the magnitude of the initial acceleration of the rod's center of mass.


I keep getting the wrong answer. Please help with a push in the right direction.
 
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  • #2
You can use the fact that the center of mass lies at 1/2 * L and that gravity grips the rod here. You can then use a simple geometric rule to find the force perpendicular to the rod, hence its initial acceleration.
 
  • #3
You can calculate the torque exerted by gravity, and hence the angular acceleration of the rod. This can be related to the linear acceleration (of for instance the CoM) by the formula
[tex] \alpha D = a[/tex]
where D is the distance to the point of interest (CoM in this example)
 

1. What is the definition of initial acceleration of a center of mass?

The initial acceleration of a center of mass is the rate at which the velocity of the center of mass changes with respect to time at the very beginning of an object's motion. It is a vector quantity that takes into account both the magnitude and direction of the change in velocity.

2. How is initial acceleration of a center of mass different from other types of acceleration?

Initial acceleration of a center of mass is specific to the beginning of an object's motion, while other types of acceleration may occur at any point during the object's motion. Additionally, initial acceleration of a center of mass takes into account the motion of the entire object, rather than just a single point on the object.

3. What factors affect the initial acceleration of a center of mass?

The initial acceleration of a center of mass is affected by the net force acting on the object, the mass of the object, and the distribution of mass within the object. Other external factors such as friction and air resistance can also play a role in the initial acceleration of a center of mass.

4. How is initial acceleration of a center of mass calculated?

The initial acceleration of a center of mass can be calculated using the equation a = F/m, where a is the acceleration, F is the net force acting on the object, and m is the mass of the object. This equation is derived from Newton's second law of motion.

5. Why is initial acceleration of a center of mass important in physics?

Initial acceleration of a center of mass is important because it helps us understand the overall motion of an object at the very beginning of its motion. It is also an important concept in analyzing the forces acting on an object and predicting its future motion. Additionally, it is a fundamental concept in classical mechanics and is used in many real-world applications, such as rocket propulsion and car design.

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