Calculating Rotational Acceleration of a Wheel

[kfish]

Homework Statement

A rotating wheel requires 3.05 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.05 s interval is 97.1 rad/s. What is the constant angular acceleration of the wheel?

Homework Equations

Well from basic calculus I know that acceleration is equal to (dV/dT) or the derivative of velocity over derivative of time.

That is the only pertinent equation I can think of for this problem.

The Attempt at a Solution

I used the velocity, 97.1 rad/s, and divided it by the time, 3.05s.

(97.1/3.05)= 31.84 rad/s^2

According to the online homework this is incorrect. I cannot think of any other way to calculate it since the radius is not given.

Homework Statement

A racing car travels on a circular track of radius 230 m. Suppose the car moves with a constant linear speed of 53.0 m/s.

(b) Find the magnitude and direction of its acceleration.

Part (a) had me calculate the velocity which came out to 0.23 rad/s. The velocity is correct.

Homework Equations

a= linear acceleration
A=rotational acceleration
R=radius

A=a/R

circumference = 2piR

The Attempt at a Solution

I figured since it says a constant linear acceleration then the angular acceleration=0 because A=(0)/(230) = 0. This answer is incorrect according to the online homework. I'm not sure what else to do.

 

[Kurdt]

The following page from hyperphysics may be of use to you.

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

 

[kerimek]

I would approach the problem by first clarifying the given information and assumptions. It is important to note that the given angular speed of 97.1 rad/s is at the end of the 3.05 s interval and the problem does not specify if the wheel started from rest or from a certain initial angular speed. This may affect the calculation of the angular acceleration.

To find the constant angular acceleration, we can use the equation:

angular acceleration (α) = change in angular speed (ω)/change in time (t)

In this case, the change in angular speed is 97.1 rad/s (final angular speed) - 0 (initial angular speed) = 97.1 rad/s. The change in time is 3.05 s. Therefore, the angular acceleration is:

α = 97.1 rad/s / 3.05 s = 31.84 rad/s^2

This is the same calculation you did, and it is correct. However, the online homework may be looking for the magnitude of the angular acceleration only, which would be 31.84 rad/s^2. The negative sign may be causing it to be marked as incorrect. In this case, the direction of the angular acceleration would be counterclockwise, as the wheel is rotating in that direction.

For the second problem, the linear acceleration of the car is given as 53.0 m/s, but we are looking for the magnitude and direction of the angular acceleration. We can use the equation:

α = a/R

Where a is the linear acceleration and R is the radius of the circular track. Plugging in the values, we get:

α = 53.0 m/s / 230 m = 0.23 rad/s^2

Again, this is the same calculation you did, and it is correct. The direction of the angular acceleration would be counterclockwise, as the car is moving in that direction along the circular track.

In summary, it is important to clarify the given information and use the appropriate equations to solve for the angular acceleration. The negative sign and direction should also be taken into account when calculating the magnitude and direction of the angular acceleration.