You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Deducing Mathematically

A solid body ...

Question

A solid body rotates about a stationary axis, according to law $θ = 6 t - {2 t}^{3}$ . What is the mean value of angular velocity, over the time interval between $t = 0$ and the time when the body comes to rest ?

2 r a d / s e c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 r a d / s e c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 r a d / s e c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 r a d / s e c

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $4 r a d / s e c$
$θ = 6 t - 2 t^{3}$
$θ_{i} = 0 r a d / s$ at $t_{i} = 0 s e c$
$θ_{f} = 6 (1) - 2 (1)^{2} = 6 - 2 = 4 r a d / s$ at $t_{f} = 1 s e c$
The average angular velocity is,
$ω_{a v g} = \frac{θ_{f} - θ_{i}}{t_{f} - t_{i}}$
$ω_{a v g} = \frac{4 - 0}{1 - 0} = 4 r a d / s$
The correct option is D.

Suggest Corrections

Similar questions

Q. A rigid body rotates about a stationary axis according to the law

θ = a t - b t^{3}

. awhere

a = 6 \frac{r a d}{s}

and

b = 2 \frac{r a d}{s^{3}}

. Then mean value of angular velocity

(ω)

over the interval

t = 0

and the moment when it comes to rest is:

Q. A solid body rotates about a stationary axis according to the law

θ = 6 t - 2 t^{3}

. Here

θ

is in radian
and

t

in seconds.
Hint: If

Y = y (t)

, then mean/average value of

y

between

t_{1}

, and

t_{2}

< Y > \frac{\int_{t_{1}}^{t_{2}} Y (t) d t}{t_{2} - t_{1}}

. The mean values of angular acceleration averaged over the time interval between

t = 0

and the complete stop is

- x

. Find

x

Q. A rigid body rotates about a stationary axis with an angular retardation

α = 4 \sqrt{ω}

, where

ω

is the angular speed of the body. Find the time after which the body will come to rest, if initially it was rotating at an angular speed of 9 rad/sec.

Q. A solid body rotates about a stationary axis according to the law

θ = 6 t - 2 t^{3}

. Here

θ

is in radian
and

t

in seconds.
Hint: If

Y = y (t)

, then mean/average value of

y

between

t_{1}

, and

t_{2}

< Y > \frac{\int_{t_{1}}^{t_{2}} Y (t) d t}{t_{2} - t_{1}}

. The angular acceleration at the moment when the body stops is

- x \sqrt{3}

. Find

x

Q. A solid body rotates about a stationary axis according to the law

φ = a t - b t^{3}

, where

a = 6.0 r a d / s

and

b = 2.0 r a d / s^{3}

Find the mean values of the angular velocity and angular acceleration averaged over the time interval between

t = 0

and the complete stop. The sum of their magnitudes is x. Find the value of x.

Join BYJU'S Learning Program

A solid body rotates about a stationary axis, according to law θ=6t−2t3. What is the mean value of angular velocity, over the time interval between t=0 and the time when the body comes to rest ?

The correct option is D 4 rad/secθ=6t−2t3θi=0rad/s at ti=0secθf=6(1)−2(1)2=6−2=4rad/s at tf=1secThe average angular velocity is,ωavg=θf−θitf−tiωavg=4−01−0=4rad/sThe correct option is D.

A solid body rotates about a stationary axis, according to law $θ = 6 t - {2 t}^{3}$ . What is the mean value of angular velocity, over the time interval between $t = 0$ and the time when the body comes to rest ?