A wheel rotates with a constant angular accel | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The angular displacement formula is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$. Given that the initial angular velocity $\omega_0 = 0

Vedclass · Accepted Answer

$1/3$

Vedclass · Answer

(C) The angular displacement formula is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$. Given that the initial angular velocity $\omega_0 = 0$,the formula simplifies to $	heta = \frac{1}{2} \alpha t^2$. For the first $2 \, s$ $(t = 2 \, s)$: ${	heta _1} = \frac{1}{2} \alpha (2)^2 = 2 \alpha$. For the total time of $4 \, s$ $(t = 2 + 2 = 4 \, s)$: ${	heta _1} + {	heta _2} = \frac{1}{2} \alpha (4)^2 = 8 \alpha$. Subtracting the first equation from the second: ${	heta _2} = 8 \alpha - 2 \alpha = 6 \alpha$. Therefore,the ratio $\frac{{	heta _1}}{{	heta _2}} = \frac{2 \alpha}{6 \alpha} = \frac{1}{3}$.

$A$ wheel rotates with a constant angular acceleration. The initial angular velocity is zero. It covers an angular displacement of ${\theta _1}$ in the first $2 \, s$ and ${\theta _2}$ in the next $2 \, s$. Then,the ratio $\frac{{\theta _1}}{{\theta _2}}$ is equal to:

Similar Questions

$A$ particle is moving with constant angular acceleration $4 \text{ rad/s}^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centripetal acceleration be equal (in $\text{ s}$)?

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. At what time will the magnitude of its centripetal acceleration and tangential acceleration be equal?

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. The time at which the magnitudes of its centripetal acceleration and tangential acceleration will be equal is (in seconds):

$A$ car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$. The angular acceleration of the wheel is ........ $rad/s^2$.

$A$ wheel of radius $0.20 \ m$ starts from rest and rotates with an angular acceleration of $1 \ rad/s^2$. What will be the centripetal acceleration of a point on its circumference when it has rotated through an angle of $90^o$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module