Need help Dynamic Problem: Plane Kinetic of rigid bodies.

In summary, the problem involves gears A and B with central moments of inertia of 10 kg.m2 and 20 kg.m2, respectively. The mass of block C is 50 kg and the system is released from rest. The goal is to determine alpha A of gear A. The equation 20 alphaB = 0.15 T is correct for alpha B, and the relationship between the two gears must be determined to solve for alpha A.
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Homework Statement



The central moments of inertia of the gears A and B as shown are 10 kg.m2 and 20 kg.m2, respectively. If the mass of the block C is mC = 50 kg and the system is released from rest, determine alpha A of the gear A

fig is attached

Homework Equations



The Attempt at a Solution



I can compute alpha B from the data but how can to compute alpha A? I mean is there an equation related between them?

By the way, about alpha B, did my equation correct?

20 alphaB = 0.15 T
T - Wc = -mC aC
aC = alphaB x 0.15

thx for your helps!

Homework Statement


Homework Equations


The Attempt at a Solution

 

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Hint:

They are gears so they rotate and accelerate at different speeds. Determine relationship.
 

1. What is a rigid body?

A rigid body is an object that cannot be deformed, meaning it maintains its shape and size regardless of external forces acting upon it. In other words, all the particles that make up a rigid body stay at a fixed distance from each other and move together as a single unit.

2. What is plane kinetic?

Plane kinetic refers to the study of motion and forces acting on objects that are constrained to move in a two-dimensional plane. This is in contrast to three-dimensional motion, which involves movement in all three spatial dimensions.

3. What are some examples of rigid bodies?

Some common examples of rigid bodies include a book, a car, a building, and a table. These objects do not deform when they are subjected to external forces, and their particles move together as a single unit.

4. How is the motion of a rigid body described?

The motion of a rigid body is described using kinematics, which involves studying the position, velocity, and acceleration of the object. It can also be described using dynamics, which involves analyzing the forces acting on the object and how they affect its motion.

5. Why is understanding the kinematics and dynamics of rigid bodies important?

Understanding the kinematics and dynamics of rigid bodies is essential in various fields of science and engineering. It allows us to accurately predict and control the motion of objects, design structures that can withstand external forces, and develop new technologies such as robotics and aerospace systems.

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