Question

A wheel turns through 2.1 revolutions while accelerating from rest at 16 rpm/s.

What is its final angular speed?

How long does it take?

Answer 1

Initial angular speed of the wheel = ₁ = 0 rad/s (Starts from rest)

Final angular speed of the wheel = ₂

Angular acceleration of the wheel = = 16 rpm/s

Converting the angular acceleration to rad/s², (1 rev = 2 rad , 1 min = 60 sec)

= 1.6755 rad/s²

Number of revolutions made by the wheel = n = 2.1 rev

Angular displacement of the wheel =

= 2n

= 2(2.1)

= 13.194 rad

₂² = ₁² + 2

₂² = (0)² + (2)(1.6755)(13.194)

₂ = 6.65 rad/s

Time taken by the wheel to complete 2.1 rev = T

₂ = ₁ + T

6.65 = 0 + (1.6755)T

T = 3.97 sec

A) Final angular speed of the wheel = 6.65 rad/s

B) Time taken by the wheel to complete 2.1 rev = 3.97 sec