16. On an amusement park ride, passengers are seated in a horizontal circle of r

Question

16. On an amusement park ride, passengers are seated in a horizontal circle of radius 11 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. What is the instantaneous tangential speed of the passengers 15 s after the acceleration begins? A) 0.067 m/s B) 0.50 m/s C) 1.4 m/s D) 7.5 m/s E) 11 m/s 17. A bicycle wheel of radius 0.70 m is rotating at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. The mass of the wheel is 2.2 kg, and its rotational inertia is 1.3 kg-m^2. What is the kinetic energy (in joules) of the wheel? A) 23 B) 28 C) 33 D) 47 E) None of these 18. A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. How many revolutions will it make in the next 8.00 seconds? A) 20 B) 40 C) 60 D) 80 E) None of these

Explanation / Answer

16) w = w0 + alpha t

1.4 = alpha*21

alpha = 1.4/21

w = 1.4*15/21= 1rad/s

v = w r = 11*1 = 11 m/s so E)

17)

KE = 1/2 mv^2 + 1/2 I w^2 = 0.5*2.2*(6.3*0.7)^2 + 0.5*1.3*6.3^2= 47 J

so D)

18)

theta = 1/2 alpha t^2

20 = 0.5*alpha*8^2

alpha = 0.625 rad/s^2

so at time = 16 s

theta = 0.5*0.625*16^2= 80 rev

so diff is 80-20 = 60

so C)

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