A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

Explanation

Supose the body is acceleratiing downward withan acceleration a

From the free body diagram
`rarr R-mg costheta=0 `
`rarr R=mg cos theta `…..i
and `ma-mg sin theta-mu R`
`=0`
`rarr a=mg(sintheta-mucostheta)/m`
`=g(sintheta-mucostheta)`
For the first halfmeter, `
v=0
S=5m, t=0.5 sec,
So, v=u+at
`=0+(0.5)4=2m/sec
From `S=ut+1/2at^2`
`0.5=0+1/2a(0.5)^2`
`rarr a=4m/s^2`
For the next half metre
`u=2m/sec, a=4m/s^2`
S=0.5
`rarr 05 =2t+(1/2)4t^2`
`rarr 2t^2+2t-05=0`
`4t^2+4t-1=0`
`rarr t=(-4+-sqrt16+16)/(2xx4)
`=1.656/8 = 0.2027`
time taken to cover next that half meter is 0.21 sec.