1D Equations of Motion

Q. When a ceiling fan is switched off, its angular velocity falls to half, while it makes $36$ rotations. How many more rotations will it make, before coming to rest?

Assume uniform angular retardation throughout the motion.

1. $36$
2. $24$
3. $18$
4. $12$

Q. A body rotating with an angular speed of $600\text{rpm}$ is uniformly accelerated to $1800\text{rpm}$ in $10\text{sec}$. The number of rotations made in the process is ____

Q.

A disc rotating about its axis and starting from rest acquires an angular speed of 100 revolutions per second in 4 s. Find the angle rotated by it during this duration.

Q. A body rotates about fixed axis with an angular acceleration of $3{\text{rad/s}}^2$. Through what angle does it rotate during the time in which its angular velocity increases from $15\text{rad/s}$ to $45\text{rad/s}$ ?

1. $300\text{rad}$
2. $100\text{rad}$
3. $150\text{rad}$
4. $200\text{rad}$

Q. A wheel is at rest. Its angular velocity increases uniformly and becomes $80$ radian per second after $5$ seconds. The angular displacement is:

1. $800\text{rad}$
2. $400\text{rad}$
3. $200\text{rad}$
4. $100\text{rad}$

Q. The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+2{\theta }_2{t}^2$. Then the angular acceleration of the body is

1. $4{\theta }_1$
2. $4{\theta }_2$
3. $2{\theta }_1$
4. $2{\theta }_2$

Q. The motor of an engine is rotating about its axis at an angular speed of $120\text{rpm}$. It comes to rest in $10\text{s}$, after being swiched off. Assuming constant acceleration, the number of revolutions made by it before coming to rest are

1. $5$
2. $10$
3. $15$
4. $20$

Q. Two wheels are mounted side by side and each is marked with a dot on its rim. The two dots are aligned with the wheels at rest, then one wheel is given a constant angular acceleration of $\frac{\pi }{2}{\text{rad/s}}^2$ and the other $\frac{\pi }{4}{\text{rad/s}}^2$. Then the two dots become aligned again for the first time after

1. 2 seconds
2. 4 seconds
3. 1 seconds
4. 8 seconds

Q.

What is the relation between $\mathrm{rad}/{\mathrm{s}}^2$ and ${\mathrm{rps}}^2$?

Q. A particle moving in a circle changes its angular velocity uniformly from $20\text{rad/s}$ to $40\text{rad/s}$ in first 5 seconds. Find the angular acceleration of the particle.

1. $2{\text{rad/s}}^2$
2. $2.5{\text{rad/s}}^2$
3. $4{\text{rad/s}}^2$
4. $3{\text{rad/s}}^2$

Q. The square of the angular velocity $\omega$ of a certain wheel increases linearly with the angular displacement during $100$ revolutions of the wheel’s motion as shown. Compute the time $t$ required for the increment.

1. $\frac{40\pi }{7}\text{sec}$
2. $\frac{20\pi }{7}\text{sec}$
3. $\frac{25\pi }{7}\text{sec}$
4. $\frac{40\pi }{3}\text{sec}$

Q. When a ceiling fan is switched off its angular velocity reduces to half of its value, while it makes $12$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

1. $18$
2. $4$
3. $24$
4. $24$

Q. An electron revolving in a circular path with initial angular velocity $6\text{rad/s}$ and constant angular acceleration of $4{\text{rad/s}}^2$. Find the ratio of ${\theta }_{5^{th}}:{\theta }_{7^{th}}:{\theta }_{9^{th}}$ (where ${\theta }_{n^{th}}$ is the angular displacement during $n^{th}$ second).

1. $1:2:3$
2. $7:9:11$
3. $5:7:9$
4. $3:4:5$

Q. A wheel is rotating at the rate of $20{\text{rev min}}^{-1}$ in clockwise direction. What should be the magnitude of the angular acceleration of the wheel so that it stops rotating in $10s$?

1. $\frac{7\pi }{24}{\text{rad s}}^{-2}$
2. $\frac{5\pi }{24}{\text{rad s}}^{-2}$
3. $\frac{7\pi }{30}{\text{rad s}}^{-2}$
4. $\frac{2\pi }{30}{\text{rad s}}^{-2}$

Q. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\text{sec}$ it rotates through an angle ${\theta }_1$, in the next $2\text{sec}$ it rotates through an additional angle ${\theta }_2$. The ratio of $\frac{{\theta }_2}{{\theta }_1}$ is -

1. $1$
2. $2$
3. $3$
4. $5$

Q. A solid body rotates about a stationary axis according to the relation $\theta =24t-2t^3$. Find the angular acceleration at the moment when body stops. (Assume SI units)

1. $-12{\text{rad/s}}^2$
2. $12{\text{rad/s}}^2$
3. $-24{\text{rad/s}}^2$
4. $24{\text{rad/s}}^2$

Q. A bike racer starting from rest is riding with constant angular acceleration on a circular track. The ratio of angular displacement of the cyclist during $5^{th}$ and $7^{th}$ second is given by

1. $7:9$
2. $4:5$
3. $8:10$
4. $9:13$

Q. When a ceiling fan is switched on it starts from rest, while completing the ${10}^{th}$ revolution it has angular velocity of $40\text{rad/s}$ , find the angular acceleration of the fan ? (Assume uniform angular acceleration)

1. $\frac{20}{\pi }{\text{rad/s}}^2$
2. $\frac{40}{\pi }{\text{rad/s}}^2$
3. $\frac{50}{\pi }{\text{rad/s}}^2$
4. $\frac{25}{\pi }{\text{rad/s}}^2$

Q. The wheel of a car accelerated uniformly from rest, rotates through $1.5\text{rad}$ during the first $\text{second}$. The angle rotated during the next $\text{second}$ will be :

1. $7.5\text{rad}$
2. $4.5\text{rad}$
3. $1.5\text{rad}$
4. $6.5\text{rad}$

Q. A grinding wheel attained a velocity of $40\text{rad/s}$ in $4s$ starting from rest. Find the number of revolutions made by the wheel.

1. $\frac{40}{\pi }$ revolutions
2. $\frac{50}{\pi }$ revolutions
3. $\frac{20}{\pi }$ revolutions
4. $\frac{25}{\pi }$ revolutions

Q. A body rotates about fixed axis with an angular acceleration of $3{\text{rad/s}}^2$. Through what angle does it rotate during the time in which its angular velocity increases from $15\text{rad/s}$ to $45\text{rad/s}$ ?

1. $300\text{rad}$
2. $100\text{rad}$
3. $150\text{rad}$
4. $200\text{rad}$

Q. A wheel rotating at a speed of $600rpm$ (revolution per minute) about its axis is brought to rest by applying a constant torque for $10$ seconds. Find the angular deceleration and the angular velocity $5$ seconds after the application of the toque.

Q. Two circular disc $A$ and $B$ with equal radii are blackened. They are heated to same temp. and are cooled under identical conditions. What inference do you draw from their cooling curves ?

1. $A$ and $B$ have same specific heats.
2. Specific heat of $A$ is less.
3. Specific heat of $B$ is less.
4. Nothing can be said.

Q. Take $z=$axis as vertical and $x-y$ plane as horizontal. A particle '$A$' is projected with velocity $4\sqrt{2}m{s}^{-1}$ making an angle ${45}^{\circ }$ to the horizontal. Particle $B$ is projected at $5m{s}^{-1}$ at an angle $\theta ={\tan }^{-1}\left(\frac{1}{3}\right)$ to $y$ axis in $y-z$ plane then velocity of $B$ wrt $A$

1. magnitude will change with time
2. has its initial magnitude $5m{s}^{-1}$
3. will initially make an angle $(\theta +\frac{\pi }{2})$ with $+x$ axis
4. lies in the $xy$ plane

Q. For a body, angular velocity $\left(\overrightarrow{\omega }\right)=\hat{i}-2\hat{j}+3\hat{k}$ and radius vector $\left(\overrightarrow{r}\right)=\hat{i}+\hat{j}+\hat{k}$, then its velocity is

1. $-5\hat{i}+2\hat{j}+3\hat{k}$
2. $-5\hat{i}+2\hat{j}-3\hat{k}$
3. $-5\hat{i}-2\hat{j}+3\hat{k}$
4. $-5\hat{i}-2\hat{j}-3\hat{k}$

Q.

A fan initially rotating at $60\text{rad/sec}$ clockwise accelerates and aquires an angular velocity of $110\text{rad/sec}$ clockwise. If the angular acceleration of fan is constant and it takes $2\text{sec}$ to change its angular velocity, find the angular acceleration of the fan.

1. $50{\text{rad/s}}^2$ in counterclockwise direction
2. $25{\text{rad/s}}^2$ in counterclockwise direction
3. $25{\text{rad/s}}^2$ in clockwise direction
4. $50{\text{rad/s}}^2$ in clockwise direction

Q. A wheel of circumference $C$ is at rest on the ground. When the wheel rolls forward through half a revolution, then the displacement of initial point of contact will be:

1. $C\sqrt{\frac{1}{{\pi }^2}+\frac{1}{4}}$
2. $\frac{C}{2}$
3. $C\sqrt{\frac{1}{\pi }+\frac{1}{2}}$
4. $\pi \sqrt{C^2+4}$

Q. In a Carnot engine, when $T_2=0^{\circ }C$ and $T_1={200}^{\circ }C$, its efficiency is ${\eta }_1$ and when $T_1=0^{\circ }C$ and $T_2={200}^{\circ }C$, Its efficiency is ${\eta }_2$, then what is ${\eta }_1$ /${\eta }_2$

1. 0.577
2. 0.733
3. 0.638
4. Can not be calculated

Q. A wind turbine is rotating with an angular velocity of $180\text{rev/min}$. It comes to rest after $5\text{mins}$. Total number of revolutions made by it before it stops (Assume angular retardation is uniform)

Q. A particle is moving along a vertical circle of radius $R$. The velocity of particle at $P$ will be : (assume critical condition at $C$)

1. $\sqrt{gR}$
2. $\sqrt{2gR}$
3. $\sqrt{3gR}$
4. $\sqrt{\frac{3}{2}gR}$