A uniform cylinder of the radius R = 3 m is spin about its axis at an angular velocity ω 0 = 40 π rad s - 1 and placed between two perpendicular walls. The coefficient of friction between the walls and cylinder is μ = 2 . Then, how many rotations will the cylinder make before it comes to rest?

Step-by-step solution

μ N 1 + N 2 = m g … … . . ( i ) N 1 = μ N 2 … … . . ( i i ) N 2 = m g 1 + μ 2 N 1 = μ m g 1 + μ 2 The torque about the center of mass of the cylinder is τ = - μ N 1 + μ N 2 R ⇒ τ = - μ m g R 1 + μ 2 μ + 1 - μ m g R μ + 1 1 + μ 2 × θ = 0 - 1 2 m R 2 2 ω 2 ⇒ θ = 1 + μ 2 R ω 2 4 μ g μ + 1 ⇒ n = θ 2 π = 1 + μ 2 R ω 2 8 π μ g μ + 1 n = 50