Question

A pulley, starting from rest, is given an acceleration of 0.5 rad/s. What will be its speed in r.p.m. at the end of 2 minutes? If it is uniformly retarded at the rate of 0.3 rad /s, in how many minutes the pulley will come to rest? is.​

Answer 1

Answer:

it is a non-uniform motion as when dividing upon 0.5/2 we get 0.25 and

when divind upon 0.3/2 we get 0.15 the two numbers 0.25 and 0.15 dont match so is non-uniform motion

Explanation:

Answer 2

the pulley will come to rest in 200sec = 3.333minutes

Explanation:

• First of all conisder angular motion of pulley at rest, iin this case

       angular velocity  $(w_{0}) =0$

       Acceleration $( \alpha _{1} )=0.51radian/sec^{2}$

      Time taken $(tx_{1} )=2minutes= 120seconds$

• Angular speed of pully in r.p.m at the end of 2min,

                    $w=w_{0} +\alpha t_{1}$

                        $=0+(0.5$×$120)$

                        $=60 radian/sec$

                        $=\frac{60}{2\pi }$

                        $= 9.55 r.p.s$

                        $= 9.55$ × $60$

                        $=573 r.p.m$

• Time in which pulley will comes to rest

          let, $t_{2}$ = time in ehich pulley comes to rest

• Now consider the angular motion of the pulley in coming to rest. In this case,

             initial angular velocity $(w_{0} )=60rad/sec$

             final angular velocity $(w)=0$

            retardation $(\alpha )_{2} =-0.3rad/sec^{2}$    [ minus sign due to retardation ]

• We knoe that final velocity of pulley

                   $0=w_{0} +\alpha t _{2}$

                     $=60-0.32t_{2}$

                 $t_{2} = \frac{60}{0.3}$

                    $= 200sec$