How much time does it take for a spinning baseball with an angular speed of 38 rad/s to rotate through 15o?

Answer 1

15° = π/12 rad

(π/12 rad)/(38 rad/s) = π/(12×38) = (π/456) ≈ 6.9 × 10^–3 sec

Answer 2

Here is the solution with detailed explanation. if you want a quick explanation, then look below after *** mark.

First, you have to convert radians to degrees or vice versa, because radians and degrees are two units of angle and one should not mix them in a single calculation.

Here it's easier to convert 15 degrees to radians.

A formula to convert degrees to radians is to multiply by π /180.

so here 15^o x π /180^o = π /12 radians.

Now the baseball is spinning at the rate of 38 rad/s.

So how long will it take to spin through π /12 rads.

This we can find by thinking in terms of ratio and proportions. If 38 rad in one second then π /12 rad in how much time.

The answer will be found by time= (π /12 rad) / (38 rad) X 1 second = π / 456 second = 0.0069 second or 6.9 ms.

***

One could also use the physics equation for angular velocity ω. θ=ω x t

here θ = π /12 rad. and ω = 38 rad/s

Solving for t, we find t= θ/ω ⇒ t = (π /12 rad) / (38 rad) = 0.0069 second or 6.9 ms.

So 6.9 ms is the correct answer.

Hope that helps.