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Brucezhou
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Could you suggest a way to solving the problem? I don't have a standard answer key and I don't know where I got wrong. I have published my method aboveehild said:How did you get your equation? It is not correct.
You have to prove that the vertical component of the acceleration of the end of the rod is greater than the acceleration of the ball. ehild
Brucezhou said:Let Wr cos(sita)=1/3 mr^2* dw/dt.
Simplify it then get:
3g*cos(sita)=r*dw/dt
Brucezhou said:Could you suggest a way to solving the problem? I don't have a standard answer key and I don't know where I got wrong. I have published my method above
weightehild said:What is W?
ehild
ehild said:The answer is written in the problem text. You do not need to solve the differential equation. As both the ball and the rod start from rest, you only need to show R what condition is the acceleration of the released ball smaller then the vertical acceleration of the end of the rod.
First you need the correct expression for the torque.
ehild
Rotational motion is the movement of an object around an axis or center point. Torque is the measure of the force that causes an object to rotate around that axis.
Linear motion involves movement in a straight line, while rotational motion involves movement around an axis. Additionally, linear motion is measured in units of distance (such as meters), while rotational motion is measured in units of angle (such as degrees or radians).
The two main factors that affect rotational motion and torque are the magnitude of the force applied and the distance between the force and the axis of rotation. Other factors that can affect rotational motion include the mass and shape of the object, as well as any external forces acting on the object.
Torque is calculated by multiplying the force applied by the distance between the force and the axis of rotation. The formula for torque is T = F * r, where T is torque, F is force, and r is the distance from the axis of rotation to the point where the force is applied.
Rotational motion and torque have many practical applications in everyday life, such as in the operation of vehicles, machines, and tools. They are also important in sports, such as in the movement of a ball in sports like basketball and soccer. In addition, rotational motion and torque are essential in the functioning of various mechanical systems, from engines to gears to propellers.