Rotational Kinematics/Tension Problem

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In summary, the question involves a cylinder with known mass, radius, and rotational inertia on an inclined plane with a string wound around it. The coefficient of static friction prevents slipping. The first part of the question asks to find the tension needed to keep the cylinder in equilibrium, while the second part asks to find the acceleration if the tension is known and different from the previous tension.
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Homework Statement


A cylinder of known mass M, radius R, and rotational inertia I is placed on an inclined plane with angle θ. A string is wound around the cylinder and pulled up with a tension T parallel to the inclined plane. The coefficient of static friction is large enough to prevent slipping.

a) Find the tension T needed to keep the cylinder in equilibrium
b) Find the acceleration of the cylinder if the tension is known and is different from T.

Homework Equations

The Attempt at a Solution

 
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Please finish the template by filling in parts 2 and 3. You can't just post the question and expect to get any help. You have to meet us half way.
 

1. What is rotational kinematics?

Rotational kinematics is the branch of physics that studies the motion of objects rotating around an axis. It involves concepts such as angular displacement, angular velocity, and angular acceleration.

2. How is rotational kinematics different from linear kinematics?

Rotational kinematics deals with the motion of objects rotating around an axis, while linear kinematics deals with the motion of objects in a straight line. This means that rotational kinematics involves concepts such as angular displacement and angular velocity, while linear kinematics involves concepts such as displacement and velocity.

3. What is the relationship between angular and linear quantities?

Angular and linear quantities are related through the radius of rotation. The linear distance traveled by an object is equal to the angle of rotation (in radians) multiplied by the radius of rotation. This relationship is known as arc length = radius x angle.

4. What is the role of tension in rotational kinematics problems?

Tension is a force that is applied to an object in order to cause it to rotate around an axis. In rotational kinematics problems, tension is often used to calculate the torque (rotational force) acting on an object, which is necessary to determine its rotational motion.

5. Can you provide an example of a rotational kinematics/tension problem?

Sure, an example problem could be: A wheel with a radius of 0.5 meters is being pulled by a rope with a tension of 20 Newtons. What is the angular acceleration of the wheel if the moment of inertia is 2 kgm^2? In this problem, tension is used to calculate the torque on the wheel, which is then used to determine the angular acceleration using the equation torque = moment of inertia x angular acceleration.

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