Angular Velocity: Find Theta at t=1 & t=5.5

In summary, The angular position of a point on the rim of a rotating wheel can be represented by the equation theta = 4*t - 3*t^2 + t^3, where theta is in radians and t is in seconds. To find the angular velocities at t = 1 and t = 5.5, you plugged in the values and got 2 and 97.625, respectively. However, after dividing by the time, you realized these values were incorrect. This is because you need to take the derivative of the position equation to find the velocity equation. Remember, calculus is necessary for this problem.
  • #1
ViewtifulBeau
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0
The angular position of a point on the rim of a rotating wheel is given by theta = 4* t - 3* t^2 + t^3, where theta is in radians if t is given in seconds.

find the angular velocities as t = 1 and t = 5.5

i plugged the numbers into the given equation to get 2 and 97.625
then i divided by the time to get 2 and 17.75 but both of these are wrong. what am i forgetting?
 
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  • #2
You are given a position equation, and you want to find the velocities at certain points in time.. do you know the relationship between position equations and velocity equations? Think calculus
 
  • #3
ahh derivitive thanks
 

Related to Angular Velocity: Find Theta at t=1 & t=5.5

1. What is Angular Velocity?

Angular velocity is a measure of how quickly an object is rotating or moving in a circular path. It is typically measured in radians per second.

2. How is Angular Velocity calculated?

Angular velocity can be calculated by dividing the change in angular displacement (theta) by the change in time. It is represented by the symbol omega (ω) and can be expressed as ω = Δθ/Δt.

3. What is Theta in relation to Angular Velocity?

Theta (θ) represents the angular displacement of an object, which is the change in its position around a fixed point. In the context of calculating angular velocity, theta represents the angle traveled by an object in a given amount of time.

4. How is Theta found at a specific time?

To find theta at a specific time, you will need to know the initial angular displacement and the angular velocity. You can then use the formula θ = θ0 + ωt, where θ0 is the initial angular displacement and t is the specific time at which you want to find theta.

5. Can Angular Velocity change over time?

Yes, angular velocity can change over time if the object's speed or direction of rotation changes. This can be represented by a change in the object's acceleration, which can be caused by external forces acting on the object.

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