Question

A disc has mass 'M' and radius 'R'. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity 'ω' in time t?

Options

• `("MR"^2omega)/"t"`

• `("MR"omega)/"t"`

• `("MR"^2omega)/"2t"`

• `("MR"omega)/"2t"`

Answer 1

`("MR"omega)/"2t"`

Explanation:

τ = I α

`therefore alpha = tau/"I" = ("F" xx "R")/("MR"^2/2) = "2F"/"MR"` = constant

`omega = omega_0 + alpha "t" = "2F"/"MR" * "t"`

`therefore "F" = ("MR"omega)/"2t"`