Question

uniform solid sphere has a mass of 1.765 kg and a radius of 0.854 m.a. Find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s, clockwise, in 15.5 s.b. What magnitude force applied tangentially at the equator would provide the needed torque

Answer 1

a) the torque required is 10.53 N-m

b) The magnitude force applied tangentially is 12.33 N

Step-by-step explanation:

Given the data in the question;

mass m = 1.765 kg

radius r = 0.854 m

first we calculate the moment of inertia;

`I` =
`(2)/(5)`mr²

we substitute

`I` =
`(2)/(5)` × 1.765 × (0.854)²

`I` = 0.514897 kg.m²

a)

Find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s, clockwise, in 15.5 s

ω
`_{initial` = 0

ω
`_{final` = 317 rad/s

t = 15.5 s

we know that; ω
`_{final` = ω
`_{initial` + ∝t

so we substitute

317 = 0 + ∝(15.5)

∝ = 317 / 15.5

∝ = 20.4514 rad/s²

so

ζ =
`I` × ∝

we substitute

ζ = 0.514897 × 20.4514

ζ = 10.53 N-m

Therefore, the torque required is 10.53 N-m

b)

What magnitude force applied tangentially at the equator would provide the needed torque.

ζ = F × r

we substitute

10.53 = F × 0.854

F = 10.53 / 0.854

F = 12.33 N

Therefore, magnitude force applied tangentially is 12.33 N