Question

The wheel of an engine starts to rotate from rest with uniform angular acceleration. It accelerates angularly for an unknown time (t1) until reaching an angular velocity of 45.13 rad / s, then maintains that angular velocity constant for 37.8 s. The total angle traveled by the wheel in total is 2398.61 rad.

a) What is the angular acceleration with which the wheel began to rotate?
b) What is the time (t1) that the wheel was accelerating?
c) What is the angle traveled by the wheel during acceleration?
d) How many laps did the wheel (revolutions) give? rev

Answer 1

(a)
Angle covered during contant velocity = 45.13 x 37.8 = 1705.914 Radian

Angle covered during acclerating time = total angle covered - angle covered during constant velocity

= 2398.61 - 1705.91

Angle covered during acclerating time = 692.7 rad (Answer of part c)

Now using 3rd equation of motion

ω^2 = ωo + 2 α θ

(45.13)^2 = 0 + (2 x α x 692.7)

2036.71 = 1385.4 α

α = 1.47 rad/s^2 (ANswer)

(b) Using 1st equation of motion

ω = ωo + α t

45.13 = 0 + 1.47 t

t = 30.7 sec (Answer)

(c)

Angle covered during contant velocity = 45.13 x 37.8 = 1705.914 Radian

Angle covered during acclerating time = total angle covered - angle covered during constant velocity

= 2398.61 - 1705.91

Angle covered during acclerating time = 692.7 rad

(d) 1 rev = 360 degree = 6.283 rad

Rev = (total angle traveled) / (angle in 1 rev)

Rev during acclerating time => 692.7 / 6.283 = 110.24 rev

Rev during constant velocity =>  1705.914 / 6.283 = 271.51 rev

Total rev = 110.24 + 271.51 = 381.75 rev