Question

A wheel has moment of inertia 5 × 10⁻³kg m² and
is making 20 rev/s. The torque needed to stop it
in 10 s is ....... × 10⁻² N-m.
(a) 2 ???? (b) 2.5 ????
(c) 4 ???? (d) 4.5 ????

Answer 1

Answer:

Initial angular velocity is ω0=20×2πrad/s=40π rad/s

The angular retardation needed to stop it in t=10sec will be given by α=tω0=40π/10=4π

So the toque needed will be 

τ=I×α=5×10−3×4π=2π×10−2N−m, 

I is the moment of inertia.

Option a is correct.

Answer 2

$\huge\underline\pink{\sf Solution:-} </p><p>$

➡I = 5 x 10^-3

➡No. of revolutions(v) = 20

➡Time =20s

➡Torque=❓

❇ Angular velocity (ω)= 2πv

➡ω = 2π x 20 = 40π rad/s

❇Angular acceleration (α)=ω/t

➡α= ω/t = 40π/ t =40π/10=4π rad/s^2

Now,

❇Torque(τ) = I x α

➡ τ = 5 x 10^-3 x 4π

➡ τ = 6.23 x 10^-3