A bicycle wheel with a radius of R = 40 cm, and it makes 100 revolutions per minute. With what angular velocity

A bicycle wheel with a radius of R = 40 cm, and it makes 100 revolutions per minute. With what angular velocity w does the wheel turn? What path S will the wheel cover in time t = 5 minutes?

R = 40 cm = 0.4 m.

N = 100.

t = 1 min = 60 s.

t1 = 5 min = 300 s.

w -?

S1 -?

The angular velocity w is expressed by the formula: w = φ / t, where φ is the turning angle, t is the turning time. In one complete revolution, the wheel turns 2 * P radians.

The angle of rotation of the wheel φ for N revolutions is φ = 2 * P * N.

The formula for the angular velocity will take the form: w = 2 * P * N / t.

w = 2 * 3.14 * 100/60 s = 10.5 rad / s.

In one complete revolution, any point of the wheel passes the circumference L1.

L1 = 2 * P * R.

S1 = L1 * N1, where N1 is the number of revolutions during time t1.

N1 = N * t1 / t.

S1 = 2 * P * R * N * t1 / t.

S1 = 2 * 3.14 * 0.4 m * 100 * 300 s * 60 s = 1256 m.

Answer: w = 10.5 rad / s, S1 = 1256 m.