(A) Given that the wheel is initially at rest,the initial angular velocity $\omega_0 = 0$.The angular acceleration $\alpha$ produced by a constant tor

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

(A) Given that the wheel is initially at rest,the initial angular velocity $\omega_0 = 0$.The angular acceleration $\alpha$ produced by a constant torque $\tau$ is given by $\alpha = \frac{\tau}{I}$.After time $t$,the angular velocity $\omega$ is given by $\omega = \omega_0 + \alpha t = 0 + \left(\frac{\tau}{I}\right)t = \frac{\tau t}{I}$.The rotational kinetic energy $K$ is given by $K = \frac{1}{2} I \omega^2$.Substituting the value of $\omega$,we get $K = \frac{1}{2} I \left(\frac{\tau t}{I}\right)^2 = \frac{1}{2} I \cdot \frac{\tau^2 t^2}{I^2} = \frac{\tau^2 t^2}{2 I}$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

Medium

$A$ wheel is at rest in a horizontal position. Its moment of inertia about the vertical axis passing through its centre is $I$. $A$ constant torque $\tau$ acts on it for $t$ seconds. The change in rotational kinetic energy is:

MHT CET 2020 All MHT CET

A
$\frac{\tau^{2} t^{2}}{2 I}$
B
$\left[\frac{\tau t}{2 I}\right]$
C
$\left[\frac{\tau t}{2 I}\right]^{\frac{1}{2}}$
D
$\left[\frac{\tau t}{2 I}\right]^{2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Relation between Torque and Angular acceleration and it's Application

Previous Year

MHT CET 2020 Paper All MHT CET years →

$A$ uniform rod of length $l$ and mass $m$ is pivoted at point $A$. The rod is released from a horizontal position. If the moment of inertia of the rod about point $A$ is $ml^2/3$,then its initial angular acceleration is:

Difficult

View Solution

In the figure $(a)$,half of the meter scale is made of wood while the other half is made of steel. The wooden part is pivoted at $O$. $A$ force $F$ is applied at the end of the steel part. In figure $(b)$,the steel part is pivoted at $O'$ and the same force $F$ is applied at the wooden end (in a horizontal plane). Which of the following is true?

Difficult

View Solution

$A$ triangular plate of uniform thickness and density rotates about an axis perpendicular to the plane of the paper. In case $(a)$,the axis passes through point $A$,and in case $(b)$,it passes through point $B$. If an equal force $F$ is applied as shown in the figure,in which case will the angular acceleration be greater?

Difficult

View Solution

$A$ torque of $50 \ N \cdot m$ causes a wheel to rotate from rest through $200 \ rad$ in $5 \ s$. The value of the angular acceleration produced is ...... $rad/s^2$.

Easy

View Solution

$A$ uniform thin rod of length $L$ and mass $m$ is lying on a smooth horizontal table. $A$ horizontal impulse $P$ is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is

MediumWBJEE 2021

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ wheel is at rest in a horizontal position. Its moment of inertia about the vertical axis passing through its centre is $I$. $A$ constant torque $\tau$ acts on it for $t$ seconds. The change in rotational kinetic energy is:

Similar Questions

$A$ uniform rod of length $l$ and mass $m$ is pivoted at point $A$. The rod is released from a horizontal position. If the moment of inertia of the rod about point $A$ is $ml^2/3$,then its initial angular acceleration is:

$A$ torque of $50 \ N \cdot m$ causes a wheel to rotate from rest through $200 \ rad$ in $5 \ s$. The value of the angular acceleration produced is ...... $rad/s^2$.

$A$ uniform thin rod of length $L$ and mass $m$ is lying on a smooth horizontal table. $A$ horizontal impulse $P$ is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is

Vedclass Test Series

Exam Paper Generator

Online Exam Module