Question

Young David, who slew Goliath, experimented with slings before tackling the giant. He found that with a sling of length 0.796 m, he could revolve the sling at the rate of 10.2 rev/s. If he increased the length to 1.14 m, he could revolve the sling only 7.3 rev/s. a) What is the larger of the two linear speeds? Answer in units of m/s.

Answer 1

given,

r₁ = 0.796 m

ω₁ = 10.2 rev/s

= (2π × 10.2) rad/s

= 64.088 rad/s

r₂ = 1.14 m

ω₂ = 7.3 rev/s

= (2π × 7.3) rad/s

= 45.87 rad/s

we know,

v = r ω

v₁ = r₁ ω₁

v₁ = 0.796 × 64.088

v₁ = 51.014 m/s

v₂ = r₂ ω₂

v₂ = 1.14 × 45.87

v₂ = 52.29 m/s