Calculating Angular Velocity and Time in a Frustrating Problem

[kiwinosa87]

This is the last problem that is frustrating me...

A wheel, starting from rest, rotates with a constant angular acceleration of 1.20 rad/s2. During a certain 5.00 s interval, it turns through 32.5 rad. (a) How long had the wheel been turning before the start of the 5.00 s interval? (b) What was the angular velocity of the wheel at the start of the 5.00 s interval?

Any help would be appreciated!

 

[chuy]

Hint:

You can apply the formula that you use for the rectilinear movement:

$$\Delta x = V_0t+\frac{1}{2}at^2$$

and

$$V_f=at$$

Replacing

$$\Delta x$$ for $$\Delta \theta$$

$$V_0$$ for $$\omega_0$$

$$\alpha$$ for a

bye

 

[kyle8921]

I understand that this problem may be frustrating, but it is important to approach it with a clear and logical mindset. To solve this problem, we can use the equation for angular displacement, θ = ω0t + 1/2αt^2, where θ is the angular displacement, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time interval.

To answer part (a), we can rearrange the equation to solve for t: t = (√(2θ/α)). Plugging in the given values, we get t = (√(2(32.5 rad)/(1.20 rad/s^2))) = 6.09 s. This means that the wheel had been turning for 6.09 s before the start of the 5.00 s interval.

For part (b), we can use the equation ω = ω0 + αt to solve for ω0, the initial angular velocity. Plugging in the values, we get ω0 = ω - αt = (1.20 rad/s^2)(6.09 s) = 7.29 rad/s. This was the angular velocity of the wheel at the start of the 5.00 s interval.

I hope this helps and remember, as a scientist, it's important to approach problems with patience and a systematic approach. Keep up the good work!