Angular Acceleration of Bicycle Wheels

In summary, the conversation involves finding the angular acceleration of a bicycle wheel with a diameter of 109.0 cm, given that the bicyclist accelerates from rest to 16.3 km/hr in 16.5 s. Using the equations w=v/r and alpha=w/t, the angular acceleration is found to be 0.5035 rad/s^2.
  • #1
rustyshackle
6
0

Homework Statement


A wheel has bicycle of diameters 109.0 cm. The bicyclist accelerates from rest with constant acceleration to 16.3 km/hr in 16.5 s. What is the angular acceleration of the wheels?



Homework Equations



w=v/r
alpha= w/t


The Attempt at a Solution



I think I'm doing it right, however, I was hoping someone might check my logic

First I convert diameter 109 cm to radius .545 m and 16.3 km/hr to 4.527 m/s.

I solve for w using linear speed divided by r = 4.527/.545 = 8.3078 rad/s

Solve for alpha using a = (wf-wi)/t = (8.3078-0)/16.5 s = .5035 rad/s^2
 
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  • #2
Your method seems good to me
 
  • #3
Thank you :)
 

1. What is Angular Acceleration?

Angular acceleration is the rate of change of angular velocity over time. In simpler terms, it is the measure of how quickly the rotational speed of an object changes.

2. How is Angular Acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The unit of measurement for angular acceleration is radians per second squared (rad/s²).

3. How does Angular Acceleration affect bicycle wheels?

Angular acceleration affects bicycle wheels by determining how quickly the wheels will rotate when a force is applied. A higher angular acceleration will cause the wheels to spin faster, while a lower angular acceleration will result in a slower rotation.

4. What factors can affect the Angular Acceleration of bicycle wheels?

The main factors that can affect the angular acceleration of bicycle wheels are the force applied to the wheels, the mass and size of the wheels, and the friction between the wheels and the ground. Other factors such as air resistance and the condition of the wheels can also play a role.

5. How can Angular Acceleration be increased on bicycle wheels?

To increase the angular acceleration of bicycle wheels, you can apply a greater force to the wheels, decrease the mass and size of the wheels, or minimize friction by using smooth tires and a well-maintained bike. Additionally, reducing air resistance by crouching or using aerodynamic equipment can also increase angular acceleration.

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