How Do You Calculate the Final Angular Velocity of a Spinning Top?

In summary, a top is a spinning toy that is controlled by pulling on a string wrapped around it. Given a string length of 64 cm and a radius of 2.0 cm, the top experiences an angular acceleration of 12 rad/s^2 when someone pulls the string. Using the equations of angular kinematics, we can determine the final angular velocity of the top when the string is fully unwound. Additionally, we can also calculate the angle that the top turns through during the unwinding process by relating angular velocity, acceleration, and distance.
  • #1
Parzival
33
0

Homework Statement



A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 64 cm and is wrapped around the top at a place where its radius is 2.0 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of 12 rad/s^2. What is the final angular velocity of the top when the string is completely unwound?

Homework Equations


Equations of angular kinematics


The Attempt at a Solution


I know that ωinitial is 0 rad/s, and that α is 12 rad/s^2, but I can't set up an equation.
 
Physics news on Phys.org
  • #2
What angle will the top turn through while the string is unwinding (i.e. while the acceleration is occurring)? How might you relate angular velocity to angular acceleration and angular distance?
 

Related to How Do You Calculate the Final Angular Velocity of a Spinning Top?

1. What is angular momentum and why is it important?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is important because it helps us understand how objects move and interact with each other in a rotational manner.

2. How do you calculate angular momentum?

Angular momentum is calculated by multiplying the moment of inertia (a measure of an object's resistance to rotational motion) by the angular velocity (the rate of change of angular displacement).

3. What are the units of angular momentum?

The units of angular momentum are kilogram meters squared per second (kg·m²/s).

4. What is the difference between linear and angular momentum?

Linear momentum is a measure of an object's motion in a straight line, while angular momentum is a measure of an object's rotational motion.

5. How is angular momentum conserved in a system?

Angular momentum is conserved in a system when there is no external torque acting on the system. This means that the total angular momentum of the system remains constant, even if individual objects within the system are rotating or moving.

Similar threads

How Do You Correctly Cancel Angular Momentum in Physics Problems?
    • Introductory Physics Homework Help
Replies
3
Views
253
Finding time in a pulley system
    • Introductory Physics Homework Help
Replies
3
Views
1K
What is the final angular velocity of each cylinder
    • Introductory Physics Homework Help
Replies
1
Views
1K
What is the angular speed of the rollers after 1.14 s?
    • Introductory Physics Homework Help
Replies
2
Views
966
Calculation of minimum angular velocity of a mass on a spinning plate
    • Introductory Physics Homework Help
Replies
2
Views
1K
Friction Torque and Lost Energy in Colliding Disks: Where Did it Go?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Using the angular momentum principle for 2 pucks
    • Introductory Physics Homework Help
Replies
3
Views
2K
Rigid Bodies/ Angular Velocity
    • Introductory Physics Homework Help
Replies
5
Views
2K
How to find Angular Speed when given frequency?
    • Introductory Physics Homework Help
Replies
4
Views
1K
Rotations from angular acceleration and final angular velocity
    • Introductory Physics Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top