Question

Young David experimented with slings before tackling Goliath. He found that he could develop an angular speed of 8.0 rev/s in a sling 0.60 m long. If he increased the length to 0.90 m, he could revolve the sling only six times per second.

(a) Which angular speed gives the greater linear speed?

Answer 1

in second case the linear speed is more.

Step-by-step explanation:

Case I

r = 0.6 m

f = 8 rev/s

ω = 2 π f

v = r x ω

v = r x 2 x π x f

v = 0.6 x 2 x 3.14 x 8

v = 30.144 m/s

Case II

r = 0.9 m

f = 6 rev/s

v = r x ω

v = r x 2 x 3.14 x f

v = 0.9 x 2 x 3.14 x 6

v = 33.9 m/s

Answer 2

Step-by-step explanation:

Given

angular speed
`N=8 rev/s`

`\omega =2\pi N`

`\omega =2\pi \cdot 8=16\pi rad/s`

length of sling
`L_1=0.6 m`

For sling length
`L_2=0.9 m`

`N_2=6 rev/s`

`\omega _2=2\pi N_2=12\pi rad/s`

Linear speed for first case
`v_1=\omega _1\cdot L_1`

`v_1=30.16 m/s`

Linear speed for Second case
`v_2=\omega _2\cdot L_2`

`v_2=12\pi \cdot 0.9=33.93 m/s`

thus case 2 gives greater linear speed