Question

A particle moves in a circle of radius 2 meters. Through what angle in radians does it rotate if it moves through an arc length of 3 meters? What is this angle in degrees?

A. 1.5rad,85.94 ∘
B. 1rad,57.3 ∘
C. 1.5rad,171.86 ∘
D. 0.75rad,42.97 ∘

Answer 1

The angle of rotation in radians for a particle moving along a 3-meter arc in a circle with a 2-meter radius is 1.5 rad, which converts to approximately 85.94 degrees.

Step-by-step explanation:

The question concerns a particle moving in a circular path and the calculation of the angle of rotation in radians and degrees. To find the angle in radians, we divide the arc length by the radius of the circle. In this case, the arc length s is 3 meters, and the radius r is 2 meters, which gives us the angle θ in radians as θ = s / r = 3 m / 2 m = 1.5 rad. To convert radians to degrees, we use the conversion factor 180°/π. Therefore, the angle in degrees is θ° = 1.5 rad × (180°/π) ≈ 85.94°.

So, the correct answer is: C. 1.5rad, 171.86°. However, there seems to be a typo in this option. The correct degree conversion, based on the radian value, should be 85.94°, not 171.86°.