Question

A solid cylinder with a radius of 73.3 cm and a mass of 2.33 kg accelerates

uniformly from rest in 4.13 seconds while experiencing 6.71 rotations.
Solve for the (a) final angular velocity.
- Solve for the (b) the torque required to produce the angular acceleration.

Answer 1

(a) 20.4 rad/s

(b) 3.09 Nm

Step-by-step explanation:

Given:

Δθ = 6.71 rev = 42.2 rad

ω₀ = 0 rad/s

t = 4.13 s

Find: ω

Δθ = ½ (ω + ω₀) t

42.2 rad = ½ (ω + 0 rad/s) (4.13 s)

ω = 20.4 rad/s

Find: α

Δθ = ω₀ t + ½ αt²

42.2 rad = (0 rad/s) (4.13 s) + ½ α (4.13 s)²

α = 4.94 rad/s²

∑τ = Iα

τ = ½ m r² α

τ = ½ (2.33 kg) (0.733 m)² (4.94 rad/s²)

τ = 3.09 Nm