Finding Angular Speed and the Change in Kinetic Energy

Thread starter dream4supreme
Start date May 19, 2019
Tags

Angular Angular speed Change Energy Kinetic Kinetic energy Speed

In summary, angular speed is the rate of change of angular displacement over time and can be measured in radians per second or revolutions per minute. It can be calculated by dividing the change in angular displacement by the change in time or by dividing the circumference of a circle by the time it takes to complete one full rotation. Angular speed is directly proportional to linear speed and kinetic energy, with the latter being directly proportional to the square of the angular speed. To calculate the change in kinetic energy when the angular speed changes, one can use the formula: change in kinetic energy = 1/2 x moment of inertia x (final angular speed)^2 - 1/2 x moment of inertia x (initial angular speed)^2.

May 19, 2019

dream4supreme

Homework Statement: A student sits on a rotating stool holding two
4 kg objects. When his arms are extended
horizontally, the objects are 0.9 m from the
axis of rotation, and he rotates with angular
speed of 0.63 rad/sec. The moment of inertia of the student plus the stool is 8 kg m2
and is assumed to be constant. The student
then pulls the objects horizontally to a radius
0.27 m from the rotation axis.
Calculate the final angular speed of the
student.
Answer in units of rad/s.

Calculate the change in kinetic energy of the
system.
Answer in units of J.

Relevant Equations: Finding Angular Speed and Change in Kinetic Energy

(4+.9)(Wf)=(4+.63)(.27)
(4.9)(Wf)=1.2501
Incorrect

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May 19, 2019

kuruman

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Your strategy for solving the problem is incomprehensible. I will not ask you to explain it, but I will ask you to consider what quantity is conserved in this case.

Related to Finding Angular Speed and the Change in Kinetic Energy

1. What is angular speed and how is it measured?

Angular speed is a measure of the rate at which an object rotates about a fixed axis. It is typically measured in radians per second (rad/s) or revolutions per minute (rpm).

2. How is angular speed related to linear speed?

Angular speed is directly proportional to linear speed, meaning that an increase in angular speed will result in a corresponding increase in linear speed. This relationship can be expressed as v = ωr, where v is linear speed, ω is angular speed, and r is the radius of the circular path.

3. What is the equation for finding angular speed?

The equation for finding angular speed is ω = Δθ/Δt, where ω is angular speed, Δθ is the change in angular displacement, and Δt is the change in time. This can also be written as ω = 2πf, where f is the frequency of rotation.

4. How is the change in kinetic energy related to angular speed?

The change in kinetic energy of a rotating object is directly proportional to the square of its angular speed. This can be expressed as ΔKE = 1/2I(ω² - ω₀²), where ΔKE is the change in kinetic energy, I is the moment of inertia, ω is the final angular speed, and ω₀ is the initial angular speed.

5. What factors affect the change in kinetic energy of a rotating object?

The change in kinetic energy of a rotating object is affected by its moment of inertia, angular speed, and any external forces or torques acting on it. The shape, size, and mass distribution of the object also play a role in determining its moment of inertia, which ultimately affects the change in kinetic energy.