all sig figs a) A motorcyclist is traveling along a road and accelerates for 6.7

Question

all sig figs

a) A motorcyclist is traveling along a road and accelerates for 6.71 s to pass another cyclist. The angular acceleration of each wheel is +7.52 rad/s2, and, just after passing, the angular velocity of each is +77.0 rad/s, where the plus signs indicate counterclockwise directions. What is the angular displacement of each wheel during this time?

b) A person is riding a bicycle, and its wheels have an angular velocity of 20.8 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 16.3 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?

c) A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.141 rad/s2. After making 2870 revolutions, its angular speed is 138 rad/s. (a)What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

Explanation / Answer

(a)  t = 6.71 s

Angular acceleration, = 7.52 rad/s^2

Angular velocity, = 77.0 rad/s

Angular displacement, is given by this formula
= t + 1/2 t^2 ----(correspond to linear motion equation, s = ut + 1/2 at^2)

= (7.52)(6.71) + (1/2) (7.52)(7.71)^2

= 50.46 + 223.51 = 273.97 radian.

(b) Here, initial velocity, vi = 20.8 rad/s
Final velocity, vf = 0 rad/s
Ang displacement, d = 16.3 rev x 2 rad/rev = 102.36 rad

Further,
d/t = average ang vel
(a) t = d / (av ang vel) = 102.36 rad / ½(20.8 + 0)rad/s

=> t = 9.84 s

(b) a = (ang vel) / t = (vf - vi) / t = (0 - 20.8rad/s) / 9.84 s

=> a = - 2.11 rad/s²

(c) (a) angular distance covered() = 2870 x 2 = 2870 x 2 x 3.14 = 18023.60 rad
By (final)^2 = (initial)^2 + 2 x x
=>(138)^2 = (initial)^2 + 2 x 0.141 x 18023.60
=>(initial) = 13961.34
=>(initial) = 118.16 rad/sec
(b) By (final) = (initial) + x t
=>138 = 118.16 + 0.141 x t
=>t = 140.71 sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.