Solve Torque Problem Set N) For Total Kinetic Energy

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In summary, Cody sits on a frictionless swivel chair with two 5lb weights on his lap, spinning with a rotation speed of 1 revolution per second. The person and chair combination can be approximated as a cylinder with a diameter of 35cm, length of 1 meter, and uniform density of 1 g/cm3. The question is what is the total kinetic energy in this rotating system. Then, Cody extends his arms to hold the weights 1 meter to his left and right, with no change in the distribution of masses. The time for 1 rotation with this distribution of masses is also asked. A sketch is requested, showing the angular vector with a magnitude in rad/sec. The final question is how much
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N) Cody sits on a frictionless swivel chair(as in the lecture hall). He rests two 5lb weights,which can be approximated as point masses, on his lap (near the axis of rotation) and pushes off to spin the assembly with a rotation speed of 1 revolution per second. Approximate the person and chair combination as a cylinder 35cm in diameter, 1 meter in length with a uniform density of 1 g/cm3. What is the total kinetic energy in this rotating system?
O) He then extends his arms to hold the 5lb weights,1 meter to his left and right as in the demo. Assume that the distribution of masses in the person and chair combination does not change by extending the arms (ie massless arms), only the position of the two 5lb point masses. What is the time for 1 rotation with this distribution of masses.
P) Make a sketch and indicate the angular vector. Indicate the magnitude in rad/sec.
Q) How much tension in the arms here leads to this centripetal acceleration of the masses. R) Show that the total kinetic energy in this rotating system is the same as in N).
 
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Related to Solve Torque Problem Set N) For Total Kinetic Energy

1. What is torque and how does it affect total kinetic energy?

Torque is the measure of the force that causes an object to rotate around an axis. It affects total kinetic energy by determining the amount of work required to change the rotational motion of an object. The greater the torque, the more kinetic energy is needed to initiate or stop the rotation.

2. How do you calculate torque in relation to total kinetic energy?

To calculate torque, you need to multiply the force applied to an object by the distance from the axis of rotation. This will give you the moment of force, which is then used to calculate the angular acceleration of the object. The total kinetic energy can be found by using the equation: KE = 1/2 * I * ω^2 (where I is the moment of inertia and ω is the angular velocity).

3. How do you determine the direction of torque and its impact on total kinetic energy?

The direction of torque is dependent on the direction of the applied force in relation to the axis of rotation. If the force is perpendicular to the axis, the torque will be maximum. The impact on total kinetic energy will be determined by the direction of the torque. A positive torque will increase the kinetic energy, while a negative torque will decrease it.

4. Can torque be negative and how does it affect total kinetic energy?

Yes, torque can be negative. This means that the direction of the applied force is opposite to the direction of rotation. A negative torque will decrease the total kinetic energy of an object, as it opposes the rotational motion.

5. How does the moment of inertia influence torque and total kinetic energy?

The moment of inertia is a measure of an object's resistance to rotational motion. A higher moment of inertia means that more torque is needed to change the object's rotational motion, resulting in an increase in total kinetic energy. Conversely, a lower moment of inertia requires less torque to change the object's rotational motion, resulting in a decrease in total kinetic energy.

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