Tangential component of linear acceleration of point on flywheel

[Hollywood]

What is the magnitude of the tangential component of the linear acceleration of a particle that is located at a distance of 50 cm from the axis of rotation when the flywheel is turning at 78.0 rev/min?

I took 78 rev/min and converted it to rad/s and got 4.08 rad/s. I then multiplied that by .5m to get my answer. Am I doing this right?

Second part: What is the magnitude of the net linear acceleration of the particle in the above question?

I don't know how I should solve this problem.

 

[Phlogistonian]

You're calculating velocity. The question is asking for acceleration.

 

[Moetasim]

I would like to clarify that the tangential component of linear acceleration refers to the acceleration of a particle along the tangent of its circular path. In this case, it would be the acceleration of the particle along the circumference of the flywheel.

To calculate the magnitude of the tangential component of linear acceleration, we can use the formula a = rω^2, where a is the linear acceleration, r is the distance from the axis of rotation, and ω is the angular velocity (in rad/s).

In the given scenario, the distance from the axis of rotation is 50 cm or 0.5 m, and the angular velocity is 4.08 rad/s. Plugging these values into the formula, we get a tangential component of linear acceleration of 8.16 m/s^2.

For the second part of the question, the net linear acceleration of the particle would also include the radial component of acceleration, which is directed towards the center of the flywheel. The magnitude of the net linear acceleration can be calculated using the formula a = √(at^2 + ar^2), where at is the tangential component of linear acceleration and ar is the radial component of acceleration.

Using the values calculated above, we can find the net linear acceleration to be approximately 8.19 m/s^2.

In conclusion, the tangential component of linear acceleration of the particle at a distance of 50 cm from the axis of rotation when the flywheel is turning at 78.0 rev/min is 8.16 m/s^2, and the magnitude of the net linear acceleration is 8.19 m/s^2.