A rod of mass m and length L, lying horizontally, is free to rotate about a vertical axis through its centre. A horizontal force of constant magnitude F acts on the rod at a distance of L/4 from the centre. The force is always perpendicular to the rod. Find the angle rotated by the rod during the time t after the motion starts

A rod of mass m and length L, lying horizontally if free to rotate about a vertical axis passing through its centre. A force F is acting perpendicular to the road at a distance L 4 from the centre. Therefore Torque about the centre due to this force, τ = F × r = F L 4 This torque will produce an angular acceleration a therefore τ c = I c × α ⇒ τ c = m L 2 12 × α ( I c of a rod = m L 2 12 ) ⇒ F L 4 = m L 2 12 × α ⇒ α = 3 F m L Therefore, θ = 1 2 α t 2 (initially at rest) ⇒ θ = 1 2 × ( 3 F m L ) t 2

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