Starting from a state of no rotation, a cylinder spins so that any point on its edge has a contant tangential acceleration of 3.1 m/s2. You keep track of the fractional number of turns N1 made made after 2.9 s and then that N2 made after 10 s. (Those numbers do not have to be integers.) What should be the approximate ratio N2/N1 ?

Explanation:

tangential acceleration at = 3.1 m  / s²

angular acceleration = tangential accn / radius

= 3.1 / r , r is radius of the cylinder .

IF N₁ be no of rotation in time t

θ = 1/2 α t² , α is angular acceleration , θ is angle in radian covered in time t

2π N₁ = 1/2 (3.1 / r ) x 2.9²

N₁ = 2.0757 / r

similarly we can calculate

2πN₂ = 1/2 (3.1 / r ) x 10²

N₂ = 24.68 / r

N₂ / N₁ = 11.89

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