An object is rotating at a constant angular velocity of 0.50 rad/s. What angle (in deg) does the object rotate through in 12 s?

Advanced Placement (AP)

1 answer:

ohaa [14]4 years ago

7 0

(0.50 rad/s) * (12 s) = 6 rad

Convert this to degrees; for every π rad, you have 180º, so

6 rad = (6 rad) * (180/π º/rad) = (1080/π)º

or about 343.76º.

You might be interested in

The acceleration, in meters per second per second, of a race car is modeled by A(t)=t3−152t2+12t+10, where t is measured in seco

iren2701 [21]

Answer:

10.237 m/s²

Explanation:

The maximum acceleration will be at one end of the interval, or at a turning point in the interval. The turning points can be found where the derivative of acceleration is zero

A'(t) = 3t^2 -304t +12

The quadratic formula will tell the zeros of this.

t = (304±√(304^2 -4(3)(12)))/(2(3)) = (304 -√92272)/6 = (152 -√23068)/3

t ≈ 0.0394891

Then the maximum acceleration is ...

A(0.0394891) ≈ 10.23690 . . . . m/s^2

<em>Additional comment</em>

The maximum magnitude of acceleration is at t=6, where acceleration is ...

A(6) = -5174 . . . . m/s^2

This is more than 500 g's in the negative direction, so the race car is not expected to survive that long.

The attached graph shows the acceleration curve for positive acceleration. The acceleration continues to decrease to a minimum of -5174 m/s^2 at the right end of the interval [0, 6].