Question
A body rotates about a fixed axis with an angular acceleration of one radian/ second/ second. Through what angle does it rotate during the time in which its angular velocity increases from 5rad/s to 15rad/s.
✓
Answer
$\alpha=1\text{rad/s}^2,\ \omega_0=5\text{rad/s};\ \omega=15\text{rad/s}$
$\therefore\text{w}=\text{w}_0+\alpha\text{t}$
$\Rightarrow\text{t}=\frac{(\omega-\omega_0)}{\alpha}=\frac{(15-5)}{1}=10\text{sec}$
Also, $\theta=\omega_0\text{t}+\frac{1}{2}\alpha\text{t}^2$
$=5\times10+\frac{1}{2}\times1\times100=100\text{rad}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
→→→→→→→→→
A block of wood is floating on water at 0°C with a certain volume x above the level of water. The temperature of water is gradually increased from 0°C to 8°C. How does the volume x change with change in temperature?
A water pump lifts water from a level 10m below the ground. Water is pumped at a rate of 30kg/ minute with negligible velocity. Calculate the minimum horsepower the engine should have to do this.
The angular frequency of damepd harmonic motion $\omega=\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}$ where $b$ is called the damping constant. Such the displacement in motion is $x =A e ^{\frac{- bt }{2 m}} \cos (\omega t +\phi)$ and retarding force $F =- b v$ where $v$ is the speed of particle. What can you say from the given equations? Can guess :
(a) How does the oscillation amplitude change?
(b) Does the period of oscillation also change with displacement?
→(a) How does the oscillation amplitude change?
(b) Does the period of oscillation also change with displacement?
Explain why
Surface tension of a liquid is independent of the area of the surface.
Surface tension of a liquid is independent of the area of the surface.
At t = 0, a particle is at rest at origin. Its acceleration is 2m/s2 for the first 3s and -2m/s2 for next 3s. Plot the acceleration versus time and velocity versus time graph.
Choose the correct alternative:
If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/ potential energy.
If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/ potential energy.
If the length of a wire increases by 1 mm when a 1 kg object is hung, then how much will the length of that wire increases when a 2 kg object is hung? How much does it hung 50 kg of weight?
Two cylinders A and B of equal capacity are connected to each other via a stop-cock. ‘A’contains a gas at S.T.P. 'B' is completely evacuated. The entire system is thermally insulated. The stop-cock is suddenly opened.
Answer the following:
- What is the change in internal energy of the gas?
- What is the change in the temperature of the gas?
In the Atwood's machine (figure), the system starts from rest. What is the speed and distance moved by each mass at t = 3s?
