Calculating Angular Speed with a Running Person on a Rotating Disk?

In summary, resulting angular speed is the measure of how fast an object is rotating or moving in a circular motion. It is different from linear speed, which refers to the speed of an object moving in a straight line. The factors that affect resulting angular speed include distance from the center of rotation, mass of the object, and force acting on the object. The formula for calculating resulting angular speed is ω = Δθ/Δt, and it can be observed in various real-life examples such as spinning a basketball, rotating a merry-go-round, and operating machines like engines and turbines.
  • #1
mparsons06
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Homework Statement



A flat uniform circular disk (radius = 2.18 m, mass = 1.22E+2 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 42.9 kg person, standing 1.29 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.20 m/s relative to the ground. Calculate the resulting angular speed of the disk (in rad/s).

I don't even know where to start. Please help?!
 
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  • #2
One hint: angular momentum.
 

FAQ: Calculating Angular Speed with a Running Person on a Rotating Disk?

What is resulting angular speed?

Resulting angular speed is the measure of how fast an object is rotating or moving in a circular motion. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

How is resulting angular speed different from linear speed?

Resulting angular speed refers to the speed of an object rotating or moving in a circular motion, while linear speed refers to the speed of an object moving in a straight line. They are both measured in different units and have different formulas for calculation.

What factors affect resulting angular speed?

The factors that affect resulting angular speed include the distance from the center of rotation, the mass of the object, and the force acting on the object. Other factors such as friction and air resistance may also affect resulting angular speed.

How is resulting angular speed calculated?

The formula for resulting angular speed is ω = Δθ/Δt, where ω is the resulting angular speed in radians per second, Δθ is the change in angle over a period of time, and Δt is the time interval. This formula can also be used to calculate resulting angular speed in degrees per second if the angle is measured in degrees.

What are some real-life examples of resulting angular speed?

Resulting angular speed can be observed in many everyday activities, such as spinning a basketball on your finger, rotating a merry-go-round, or swinging a bat. It is also crucial in more complex systems such as engines, turbines, and gears in machines.

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