Question

 1. A bicycle slows down uniformly from an initial velocity vi = 8.70 m/s to rest over a distance of 125 m. Each wheel has an overall diameter of 690 cm. You can assume that the wheels roll without slipping. 

(a) Calculate the angular speed of the wheels at the initial instant (t = 0). 

(b) Calculate the total number of revolutions each wheel rotates before coming to rest. 

(c) Calculate the angular acceleration of the wheel 

(d) Calculate the time it takes to come to a stop. 

2. Astronauts often have to train in high-8 (high gravity) environments before they embark on space missions. A space-training module consists of a capsule that rotates insides a horizontal circular track of radius 115 m. The rotational speed increases at a constant rate from rest such that the capsule finishes its first cycle in 8.00 s. 

(a) How long does it take from the start of the motion for the radial acceleration to be equal to five times the acceleration due to gravity. 

(b) How long does it take for the radial acceleration to be equal in magnitude to the tangential acceleration? 

Answer 1

Initial velocity u=8.90 m/s finell velocity v= 0 displecement s=125m v²= u²+zas 0 = (8.7)*+2a (125) a=-0.30276 m/s² (-ve for direction) @ wale 1. Ans. Auguler speed (w)= 8.7 rand/ = 0.69 15 = 12.61 reals (2 ar)n=125 No. of revolution (2)= -1 125 21 (0.69) = 28.83 revolutions. Ans Angules aueleration a= a -0.30276 6 = -0.4388 reel/2 Aug 0.69 v=ut at 0 = 8.7+(-0.30276)+ t = 8.7 -0.30270= 28.74 see. Am