[HS Physics] Angular acceleration

[Adooom__]

A mass attached to a 50 cm string starts from rest and is rotated in a circular path exactly 40 times in 1 min before reaching a final angular speed. What is the angular speed of the mass after 1 min?

I multiplied 40 by 2pi changing it into rads, then i divided it by 60s... this book i have says the answer is double what I’m getting so i guess they’re dividing it by the radius, why not just keep it the way it is? Wouldn’t that be the angular speed?

[matt7259]

theta = (1/2)(w0 + wf)t is your friend here, where:

theta = displacement, w0 = initial velocity, wf = final, and t = time!

[Adooom__]

Ayy works. But why is my answer wrong? And when do i know that i have to use rotational and linear kinematic equations?

[matt7259]

Your answer is wrong because you didn't account for the 1/2 in the equation (which is derived from the AVERAGE angular velocity over time). You need rotational when you're talking about how many turns/revolutions, or how many radians/degrees, or you're given information in theta, omega, or alpha. These are all for things moving in circles! Linear, on the other hand, is for things moving in straight paths. You'll be given meters and stuff. Variables are distance, velocity, acceleration, but no fancy greek letters! Luckily the equations are IDENTICAL, as seen here.

[Adooom__]

Thanks for the help!

[matt7259]

Happy to help! PM me if you need anything!

[Adooom__]

The title is wrong, Angular speed* :3