What Equations Calculate Tangential Acceleration Correctly?

[pennyfx]

A disk of radius .12 m starts accelerating from rest at 8 rad/s^2 At t = 5s

A)What is the Angular Velocity
This one is easy.. Av = 8rad/s^2*5 = 40 rad/s
And makes sense.

B)What is the tangential Accel?The book gave answer of .96 m/s^s Therefor, i assumed that the equation is At = w*r w=omega which is 8 rad/s^2 * .12m = .96 m/s^2

However, later I found an equation for At given as At=dv/dt
What gives? Which equation is correct for Tangential Accel? If they are both correct then how would I use At=dv/dt?


Thanks

 

[Gopi Prashanth]

Both are correct,

Remember dv/dt is nothing but d(r*Av)/dt and since r is constant r*d(Av)/dt
which is nothing but r*w... which was the first equation you used...

 

[wais]

for your question! Both equations for tangential acceleration are correct, but they are solving for different things. The equation At = w*r is solving for the tangential acceleration at a specific point in time, while the equation At = dv/dt is solving for the change in tangential velocity over time.

In this specific scenario, the tangential acceleration at t = 5s is 0.96 m/s^2, as calculated using At = w*r. This tells us how much the tangential velocity is changing at that specific moment in time.

On the other hand, if we were to use At = dv/dt, we would be solving for the average tangential acceleration over a period of time. This equation takes into account the change in tangential velocity over that time period, rather than just at a specific moment.

Both equations are correct and can be used depending on what information you are trying to find. If you are trying to find the tangential acceleration at a specific moment in time, use At = w*r. If you are trying to find the average tangential acceleration over a period of time, use At = dv/dt.