I don't know how to solve this problem.

Question

a cylinder is rotating about an axis that passes through the center of each circular end piece. the cylinder has a radius of 0.0830 m. an angular speed of 76.0 rad/s, and a moment of inertia of 0.615 kgm². A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. the frictional force reduces the angular speed of the cylinder by a factor of two during a time of 6.40 s. (a) find the magnitude of the angular deceleration of the cylinder. (b) find the magnitude of the force of friction applied by the brake

Answer 1

The key to rotational problems is understanding the analogy between translational equations and rotational equations. Kinematics: rot var * R = var at rim and Dynamics I is substituted for m. Also, torque is F x Lever arm and angular momentum is F x mv.

a) You are given ω₀, ω = ω₀/2, t = 6.4 s so you can find α (const acceleration process)

By analogy with v = v₀ + at , you write ω = ω₀ + αt or α = (ω-ω₀)/t in rad/s² Depending on your teacher, deceleration can be positive, but the equation will give a negative rotational acceleration because ω < ω₀

b) Now, by analogy to F = ma , you write τ = Iα substitute in τ=FR and I = 1/2 MR² for the cylinder and you get FR = 1/2 MR²α

I'll leave you to do the rest, Solve for F given all the rest and your answer to (a). Note that the force will be negative.