Angular Velocity and Acceleration Problem

In summary: It will be the same time for which speed is increasing. So, speed of the wheel will be increasing for 3.5 seconds and decreasing for 3.5 seconds.c.) What is the angular displacement of the whee at t = 7.00s?In summary, the wheel is rotating about an axis in the z-direction with an initial angular velocity of -6.00 rad/s at t=0. The angular velocity increases linearly with time and reaches +8.00 rad/s at t=7.00s. The angular acceleration during this time interval is positive. The speed of the wheel is increasing for 3.5 seconds and decreasing for 3.5 seconds. The angular displacement of
  • #1
iwonde
31
0
A wheel is rotating about an axis that is in the z-direction. The angular velocity w_z is -6.00 rad/s at t=0, increases linearly with time, and is +8.00 rad/s at t =7.00s. We have taken counterclockwise rotation to be positive.

a.) Is the angular acceleration during this time interval positive or negative?

b.) During what time interval is the speed of the wheel increasing? Decreasing?

c.) What is the angular displacement of the whee at t = 7.00s?

a.) Angular acceleration is positive because alpha = (delta omega)/ delta t = 2 rad/s^s
b.) I'm not sure of how to approach this part. My guess is that the speed is increasing when the rotation is counterclockwise and decreasing when it's clockwise. I need help with this one.
c.) I just plugged t=7s into the equation φ(t) = φ_0 + (ω_0)t + (1/2)αt^2 and I got 7.00 rad.
 
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  • #2
If one draws a rough sketch of the angular acceleration of the wheel as a function of time it will form a linear graph. This graph stretches from -6 at t = 0 to +8 at 7 s. The (angular and linear) speed of the wheel decreases up to the point where this graph crosses the time axis. Thereafter it increases. That is it first slows down and momentarily stops rotating. Then its speed increases in the opposite direction.
 
  • #3
iwonde said:
a.) Is the angular acceleration during this time interval positive or negative?
The angular velocity changes from -ve to +ve therefore the angular acceleration is +ve.


b.) During what time interval is the speed of the wheel increasing? Decreasing?
When the direction of motion of that wheel changes, it will be at rest for an instant.
Use [tex]\omega=\omega_o + \alpha t[/tex]
with [tex]\omega=0[/tex] and [tex]\omega_o = -6[/tex]
This will give the time for which speed is decreasing.
 

1. What is Angular Velocity?

Angular velocity is a measure of how quickly an object rotates around a fixed point, such as an axis. It is typically expressed in radians per second or revolutions per minute.

2. How is Angular Velocity different from Linear Velocity?

Angular velocity and linear velocity are both measures of an object's speed, but they differ in the direction of movement. Linear velocity refers to the speed of an object in a straight line, while angular velocity refers to the speed of an object in a circular path.

3. How is Angular Velocity calculated?

Angular velocity can be calculated by dividing the change in angle by the change in time. The formula is: ω (angular velocity) = Δθ (change in angle) / Δt (change in time).

4. What is Angular Acceleration?

Angular acceleration is a measure of how quickly the angular velocity of an object changes over time. It is typically expressed in radians per second squared or revolutions per minute squared.

5. How is Angular Acceleration related to Angular Velocity?

Angular acceleration and angular velocity are closely related. Angular acceleration is the rate of change of angular velocity, meaning that it describes how quickly the angular velocity is changing. A positive angular acceleration means that the angular velocity is increasing, while a negative angular acceleration means that the angular velocity is decreasing.

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