A wheel is spinning about a fixed axis in a clockwise direction at 20.0 revolutions per minute. There is a spot of paint on the wheel located 20.0 cm from the axis of rotation. Disregarding the phase of the motion and with the origin located at the center of the wheel, which of the following is a description of the motion of the paint spot projected onto a given direction in the plane of motion? A)x(t) = (20.0 cm)cos[(2.09 s^-¹)t] B)x(t) = (40.0 cm)cos[(0.333 s^-¹)t] C)x(t) = (20.0 cm)cos[(0.333 s^-¹)t] D)x(t) = (20.0 cm)cos[(20.0 s^-¹)t] E)x(t) = (40.0 cm)cos[(126 s^-¹)t]

Question

Quizplus · Accepted Answer

The correct answer is A because the wheel is spinning at 20.0 revolutions per minute, which means that it is completing 20.0 revolutions in 60.0 seconds. Therefore, the angular velocity of the wheel is 20.0 revolutions per minute / 60.0 seconds = 2.09 radians per second. The spot of paint is located 20.0 cm from the axis of rotation, which means that the radius of the circle that the spot of paint is moving in is 20.0 cm. Therefore, the position of the spot of paint projected onto a given direction in the plane of motion is given by x(t) = (20.0 cm)cos[(2.09 s^-¹)t].

A Wheel Is Spinning About a Fixed Axis in a Clockwise