Angluar Velocity and Revolutions

In summary, angular velocity is the rate of change of angular position of an object with respect to time and is measured in radians per second or degrees per second. It differs from linear velocity in that it takes into account the distance from the center of rotation. RPM is a unit of measurement for angular velocity and an increase in angular velocity can result in a higher centrifugal force. Factors such as moment of inertia, torque, and external forces can affect the angular velocity of an object, as well as friction and air resistance.
  • #1
Jar9284
3
0

Homework Statement


You switch a food blender from its high to its low setting; the blade speed drops from 3100 rpm to 1300 rpm in 2.1 s. How many revolutions does it make during this time?

Homework Equations


[tex]\omega[/tex]i = [tex]\frac{3100 rpm * (2 * pi)}{60}[/tex] = 324.6 rad/sec
[tex]\omega[/tex]f = [tex]\frac{1300 rpm * (2 * pi)}{60}[/tex] = 136.1 rad/sec

[tex]\omega[/tex]f = [tex]\omega[/tex]i + [tex]\alpha[/tex]t

[tex]\omega[/tex]f[tex]^{2}[/tex] = [tex]\omega[/tex]i[tex]^{2}[/tex] + 2[tex]\alpha[/tex]([tex]\Delta[/tex][tex]\Theta[/tex])

The Attempt at a Solution



136.1 = 324.6 + 2.1 [tex]\alpha[/tex]

[tex]\alpha[/tex] = 89.8 rad/sec[tex]^{2}[/tex]

136.1[tex]^{2}[/tex] = 324.4[tex]^{2}[/tex] + 2 * 89 ([tex]\Delta[/tex][tex]\Theta[/tex])

([tex]\Delta[/tex][tex]\Theta[/tex]) = 482.8 rad / (2 * pi) = 76.8 rev

Want to make sure if this is correct.
 
Physics news on Phys.org
  • #2
Looks good to me :)
 
  • #3




Your calculation appears to be correct. The change in blade speed from 3100 rpm to 1300 rpm in 2.1 seconds can be expressed as a change in angular velocity, which is represented by the Greek letter omega (\omega). Using the given formula for angular velocity, you correctly calculated the initial and final angular velocities as 324.6 rad/sec and 136.1 rad/sec, respectively.

To determine the number of revolutions made during this time, you used the formula for rotational motion, where the final angular velocity is equal to the initial angular velocity plus the product of angular acceleration (\alpha) and the change in time (\Delta t). You correctly solved for angular acceleration as 89.8 rad/sec^2.

Next, you used the formula for kinetic energy in rotational motion, where the final angular velocity squared is equal to the initial angular velocity squared plus twice the product of angular acceleration and the change in angular displacement (\Delta\Theta). Solving for \Delta\Theta, you correctly calculated the number of revolutions as 76.8 rev.

Overall, your solution is correct and demonstrates a good understanding of the concepts of angular velocity and revolutions in rotational motion. Keep up the good work!
 

FAQ: Angluar Velocity and Revolutions

What is angular velocity?

Angular velocity refers to the rate of change of angular position of an object with respect to time. It is measured in radians per second (rad/s) or degrees per second (deg/s).

How is angular velocity different from linear velocity?

Angular velocity is a measure of the rotational speed of an object, while linear velocity is a measure of the speed at which an object is moving in a straight line. Angular velocity takes into account the distance from the center of rotation, while linear velocity does not.

What is the relationship between angular velocity and revolutions per minute (RPM)?

RPM is a unit of measurement for angular velocity. One revolution per minute is equal to 2π radians per minute. This means that the angular velocity in radians per second can be calculated by dividing the RPM by 60.

How does angular velocity affect centrifugal force?

Centrifugal force is the outward force experienced by an object rotating around a center point. The magnitude of this force is directly proportional to the angular velocity of the object. This means that an increase in angular velocity will result in a higher centrifugal force.

What factors can affect the angular velocity of an object?

The angular velocity of an object can be affected by its moment of inertia (which depends on its mass and distribution of mass), the applied torque, and any external forces acting on the object. Friction and air resistance can also affect the angular velocity of an object.

Back
Top