Question

A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2 rad/s2 and is slowing at first. What time elapses before its angular velocity is 22 rad/s in the direction opposite to its initial angular velocity?​

Answer 1

Answer:

ANSWER

Given initial angular velocity ω

i

=18 rad/s

final angular velocity ω

f

=−18 rad/s

And we know acceleration α=

t

ω

f

−ω

i

=

t

−18−18

t=

2

−36

=−18=18 s

December 27, 2019

avatar

Toppr

Answer 2

Answer:

The time taken by the wheel, t, calculated is $20sec$.

Explanation:

Given data,

The initial angular velocity of the wheel, ω₁ = $18rad/s$

The constant angular acceleration, α = $-2rad/s^{2}$ ( in opposite direction )

The final angular velocity of the wheel, ω₂ = $-22rad/s$ ( as the direction is opposite)

The time taken by the wheel, t =?

As we know,

• The angular acceleration, α = $\frac{\omega_{2}-\omega_{1} }{t}$

Therefore,

• t = $\frac{\omega_{2}-\omega_{1} }{\alpha }$
• t = $\frac{-22-18}{-2}$ = $\frac{40}{2}$ = $20sec$

Hence, the time taken by the wheel, t = $20sec$.