Angular Velocity & Angular Acceleration

In summary, a person is riding a bicycle with an angular velocity of +19.5 rad/s. The brakes are applied and the bike comes to a uniform stop with an angular displacement of +11.5 revolutions for each wheel. Using the equations avg ang. v=ang. x/t and avg ang. a=change in ang. v/t, the time it takes for the bike to come to rest is approximately 3.71 seconds and the angular acceleration of each wheel is 5.27 rad/s^2. The solution was found by considering the bike's deceleration as a non-uniform angular velocity problem.
  • #1
ladolce
56
0

Homework Statement



A person is riding a bicycle, and its wheels have an angular velocity of +19.5 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is +11.5 revolutions.

(a) How much time does it take for the bike to come to rest?

(b) What is the angular acceleration of each wheel?

Homework Equations



avg ang. v=ang. x/t

avg ang. a=change in ang. v / t

The Attempt at a Solution



I plugged in and got...

delta theta=11.5 x 2pi=72.26 radians

and

72.26rad/(t) = 19.5

and so t=3.7 or 3.706 or 3.71 and all those are wrong... I don't know what i did wrong.
 
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  • #2
You are treating this as problem with uniform angular velocity. Clearly that's not true since the bike is slowing down. You need the analog of x(t)=x0+v0*t+(1/2)*a*t^2. Remember linear motion?
 
  • #3
thanks i got the problem right after i typed it though =)
 

1. What is the difference between angular velocity and angular acceleration?

Angular velocity refers to the rate of change of angular displacement, while angular acceleration is the rate of change of angular velocity. In simpler terms, angular velocity tells us how fast an object is rotating, while angular acceleration tells us how quickly the rotation is changing.

2. How are angular velocity and linear velocity related?

Angular velocity and linear velocity are related through the formula: v = rω, where v is linear velocity, r is the distance from the axis of rotation to the object, and ω is the angular velocity. This means that as the distance from the axis of rotation increases, the linear velocity also increases.

3. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. This can be represented by the formula: α = Δω/Δt. Angular acceleration is typically measured in radians per second squared (rad/s²).

4. What factors affect angular velocity and angular acceleration?

Angular velocity and angular acceleration are affected by the radius of rotation, the mass of the object, and the applied torque. A larger radius of rotation and a larger mass will result in a higher angular velocity and acceleration, while a larger applied torque will result in a higher angular acceleration.

5. How does angular acceleration affect rotational motion?

Angular acceleration is responsible for changing the rotational motion of an object. A positive angular acceleration causes an increase in angular velocity, while a negative angular acceleration causes a decrease in angular velocity. Without angular acceleration, an object will maintain a constant angular velocity and thus continue rotating at a constant rate.

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