Angular Acceleration of a bicycle

In summary, the bicyclist accelerates from rest to a speed of 6.1 m/s in 13.7 seconds, resulting in an angular velocity of 15.278 radians. To determine the angular acceleration of the wheels, the formula alpha = omega/t can be used.
  • #1
maniacp08
115
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A bicycle has wheels of 0.8 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 13.7 s. What is the angular acceleration of the wheels?

relevant equations:
omega = omega initial + alpha * t

22km/h = 6.11m/s

I did 6.11m/s * 13.7s = 83.7207 to get the velocity
then I divided it by .4m to get 209.30175
Im not sure what I should do nextI have another question which is related to the same topic:
A block of 2kg falls with a speed of 3.9m/s from rest to a distance of 2.5m, its acc. is 3.0m/s from a pulley of radius of 8cm.

(b) What is the angular velocity of the pulley at this time?
I used V = R/omega
= 3.9m/s = .08m / omega
omega = .02
This is wrong is my approach wrong?
 
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  • #2
maniacp08 said:
A bicycle has wheels of 0.8 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 13.7 s. What is the angular acceleration of the wheels?

relevant equations:
omega = omega initial + alpha * t

I did 22km/hr * 13.7s = 301.4 km s / hr to get the velocity
Vi = 0
Im not sure what I should do next

First convert km/h to m/s = 1000/3600

v = 22 kmph = 6.1 m/s

w = v/r = 6.1/.4 = 15.278 radians

w = a*t => a = w/t = ... ?
 
  • #3


I would like to clarify that the angular acceleration of a bicycle is not a well-defined concept. Angular acceleration is typically used to describe the rate of change of angular velocity, which is the rotational speed of an object. In the case of a bicycle, the wheels do rotate, but the entire bicycle is also moving in a linear direction. Therefore, it is more appropriate to use linear acceleration to describe the motion of the bicycle.

To calculate the linear acceleration of the bicycle, we can use the equation a = (v - v0)/t, where a is the acceleration, v is the final velocity, v0 is the initial velocity, and t is the time. Plugging in the given values, we get a = (6.11 m/s - 0 m/s)/13.7 s = 0.446 m/s^2. This is the linear acceleration of the bicycle.

For the second question, the approach used to calculate the angular velocity of the pulley is incorrect. The equation V = R/omega is used to calculate the tangential velocity of a point on a rotating object, not the angular velocity itself. To calculate the angular velocity, we can use the equation omega = v/R, where omega is the angular velocity, v is the tangential velocity, and R is the radius of the pulley. Plugging in the given values, we get omega = 3.9 m/s / 0.08 m = 48.75 rad/s.
 

What is angular acceleration of a bicycle?

Angular acceleration of a bicycle is the rate of change of its angular velocity over time. It describes the change in the direction or magnitude of the bicycle's rotational motion. It is measured in radians per second squared.

How is angular acceleration of a bicycle calculated?

Angular acceleration of a bicycle can be calculated by dividing the change in its angular velocity by the time interval over which the change occurred. It can also be calculated by taking the second derivative of the bicycle's angular position with respect to time.

What factors affect the angular acceleration of a bicycle?

The angular acceleration of a bicycle is affected by several factors such as the mass and distribution of mass of the bicycle, the force applied to the pedals, the friction of the tires on the ground, and the air resistance. The shape and size of the bicycle also play a role in its angular acceleration.

How does angular acceleration affect the motion of a bicycle?

The angular acceleration of a bicycle determines how quickly it can change its direction or speed while in motion. A higher angular acceleration allows the bicycle to turn more sharply or accelerate more quickly, while a lower angular acceleration results in slower turns and acceleration.

What is the difference between angular acceleration and linear acceleration of a bicycle?

Angular acceleration describes the change in the bicycle's rotational motion, while linear acceleration describes the change in its linear motion. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared. Both types of acceleration can occur simultaneously in a bicycle's motion.

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