ahh i need help with my physics homework and its due in 3 days

Question

A uniform disk with a mass of 180 kg and a radius of 1.4 m rotates initially with an angular speed of 1150 rev/min. A constant tangential force is applied at a radial distance of 0.8 m.

a) How much work must this force do to stop the wheel? Answer in units of kJ.

b) If the wheel is brought to rest in 4 min, what torque does the force produce? Answer in units of N · m.

c) What is the magnitude of the force? Answer in units of N.

d) How many revolutions does the wheel make in these 4 min? Answer in units of rev.

Answer 1

First, convert rpm to initial angular velocity ω_o = (1150 rev/min)*(2π rad/rev)*(1 min/60 s) = 120.4 rad/s.

a) The work will be to cancel out the rotational kinetic energy (1/2) I ω², where I = (1/2) M R² for uniform disk. I = (1/2)*(180 kg)*(1.4 m)² = 176.4; RKE = (1/2)*(176.4)*(120.4)² = 1,280 kJ, so work = -1,280 kJ.

b) Δt = 4 min = 240s, and use ω_f = ω_o + α Δt = 0 to find angular acceleration α = -(120.4)/(240) = -0.5018 rad/s². From τ = Iα, torque = -(176.4)*(0.5018) = -88.5 Nm.

c) Since torque = force*lever arm, magnitude of F = |τ/0.8| = 111 N.

d) Use angular displacement θ = (1/2)*(ω_o + ω_f) Δt = (1/2)*(120.4 + 0)*(240) = 14,448 radians *(1 rev/2π rad) = 2,299 revolutions.