Rotational kinematics and grinding wheel

[ACLerok]

i've been doing some physics problems out of the text and I was wondering: If an electric fan were to be turned off and you knew its angular acceleration, it is possible to find the number of revolutions it makes in a certain time interval?

also, i having a difficult time with this problem.

At t=0 a grinding wheel has an angular velocity of 22. rad/s. It has a constant angular acceleration of 32. rad/s^2 until a circuit breaker trips at time t=1.7 s. From then on, it turns through an angle 433. rad as it coasts to a stop at constant angular acceleration.
I was able to find the total angle the wheel had turned between t=0 to the time it comes to a rest to be 516.64 rad, but now i have to find at what exact time it comes to a stop.. any pointers and tips are greatly appreciated.

thanks

 

[ShawnD]

Originally posted by ACLerok
At t=0 a grinding wheel has an angular velocity of 22. rad/s. It has a constant angular acceleration of 32. rad/s^2 until a circuit breaker trips at time t=1.7 s. From then on, it turns through an angle 433. rad as it coasts to a stop at constant angular acceleration.
I was able to find the total angle the wheel had turned between t=0 to the time it comes to a rest to be 516.64 rad, but now i have to find at what exact time it comes to a stop.. any pointers and tips are greatly appreciated.

thanks

1. find the rotation speed when the breaker tripped (Wf = Wi + a*t)
2. find the deceleration from when breaker tripped (Wf^2 = Wi^2 + 2ad)
3. find the time it took took to decelerate (d = Wi*t + (1/2)a*t^2)

That should work.

 

[M98Ranger]

Yes, it is possible to find the number of revolutions a fan makes in a certain time interval if you know its angular acceleration. This can be done by using the equation:

Δθ = ω0t + 1/2αt^2

Where Δθ is the total angle turned, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time interval.

In the case of the grinding wheel problem, you can use the same equation to find the time it takes for the wheel to come to a stop. You already have the values for ω0, α, and Δθ, so you can rearrange the equation to solve for t. Once you have the time, you can subtract 1.7 seconds (the time when the circuit breaker trips) to find the exact time the wheel comes to a stop.

As for tips, make sure to pay attention to the units of your values. In this problem, the units for angular velocity and acceleration are in radians per second and radians per second squared, respectively. Also, double check your calculations and make sure to use the correct formula for the given scenario. Keep practicing and you will get better at solving these types of problems. Good luck!