With uniform rotation, one wheel makes N1 = 240 revolutions in a time t1 = 8 s, and the second makes N2 = 600

With uniform rotation, one wheel makes N1 = 240 revolutions in a time t1 = 8 s, and the second makes N2 = 600 revolutions in a time t2 = 40 s. How many times do their angular velocities differ?

t1 = 8 s.

N1 = 240.

t2 = 40 s.

N2 = 600.

w1 / w2 -?

The angular velocity w is the ratio of the angle of rotation ∠α of the wheel to the time t during which this rotation is completed: w = ∠α / t.

w1 = ∠α1 / t1.

w2 = ∠α2 / t2.

Since the angle of one complete rotation is ∠α = 2 * п radians, the wheels make respectively N1 and N2 full revolutions, then ∠α1 = N1 * 2 * п, ∠α2 = N2 * 2 * п.

w1 = N1 * 2 * п / t1.

w2 = N2 * 2 * п / t2.

w1 / w2 = N1 * 2 * п * t2 / t1 * N2 * 2 * п = N1 * t2 / t1 * N2.

w1 / w2 = 240 * 40 s / 8 s * 600 = 2.

Answer: the angular velocity of the first wheel w1 is 2 times greater than the angular velocity of the second wheel w1: w1 / w2 = 2.