Angular Displacement

Q. if the radius of th earth is 6400 km, then its angular velocity

Q. Why is the angular displacement a vector quantity for small value of theta and why it is a scalar quantity for big value of theta? Explain elaborately.

Q. A student runs $120\text{m}$ around a circular track of $40\text{m}$ radius. What is her angular displacement?

1. 1 rad
2. 2 rad
3. 3 rad
4. 4 rad

Q.

The angular displacement θ of a fly wheel at the instant t is given by

θ = 2t³ - 4 t² + 8

The angular acceleration of the fly wheel after 2s is

1. 16 rad/s²

2. 8 rad/s²

3. 12 rad/s²

4. 20 rad/s²

Q. Vo= √3gl And R= l. What is the maximum vertical displacement ?

Q. Find the angular displacement of the hour hand of a normal clock in $4\text{h}$

1. $\frac{\pi }{3}$
2. $\frac{\pi }{6}$
3. $\frac{2\pi }{3}$
4. $\frac{3\pi }{2}$

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

1. 1
2. 2
3. 3
4. 4

Q. A wheel starting from rest, rotates with a uniform angular acceleration of $2{\text{rad/s}}^2$. The number of rotation it performs in the tenth second is

1. 3
2. 6
3. 9
4. 12

Q. When a wheel completes $2000$ revolutions to cover $15\text{km}$ distance, then the radius of the wheel is?

1. $1.19\text{m}$
2. $2\text{m}$
3. $2.4\text{m}$
4. $0.8\text{m}$

Q. Find out the dimensional formula for following quantity: 1) Angular displacement and 2) Angular velocity

Q. A spotlight is fixed $4\text{m}$ from the vertical wall and is rotating at a rate ${\text{1 rads}}^{-1}$. The spot moves vertically on the wall. Find the speed ( in ${\text{ms}}^{-1}$) of the spot on the wall when the spotlight makes an angle of ${45}^{\circ }$ with the wall.

Q. 10. Are the magnitude and directionof (vector A-vectorB) and ( vectorB - vectorA) same? why.

Q. Why is the angular displacement a vector quantity for small value of theta and why it is a scalar quantity for big value of theta? Explain elaborately.

Q. For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then, the angle of inclination of the inclined plane is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. Calculate the ratio of angular speed of rotation of earth and hour hand of 12hour clock

Q. F= yi^ + xj^ Displacement from (0, 0)--‐---->(2, 4). Find work? W=∫F•dr

Q. A stone tied to an inextensible string of length $l=1\text{m}$ is kept horizontal. If it is released, find the angular speed (rad/s) of the stone when the string makes an angle $\theta ={30}^{\circ }$ with horizontal.

1. $3.16$
2. $3$
3. $2.28$
4. $4.16$

Q. The magnitude of the displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

1. $2asin\omega t$
2. $2asin\frac{\omega t}{2}$
3. $2acos\omega t$
4. $2acos\frac{\omega t}{2}$

Q. The angular position of one of the blades of a fan is ${\theta }_1=\frac{\pi }{3}\text{rad}$, as shown in the figure. If the fan is switched on and off within a fraction of a second, the blade’s angular position changes to ${\theta }_2=\frac{\pi }{2}\text{rad}$. The angular displacement of all the blades is

1. $\frac{\pi }{6}\text{rad}$
2. $\frac{\pi }{4}\text{rad}$
3. $\frac{\pi }{6}\text{degrees}$
4. $\frac{\pi }{4}\text{degrees}$

Q. A student runs $120\text{m}$ around a circular track of $40\text{m}$ radius. What is her angular displacement?

Q. A person covers $\frac{1}{3}rd$ of a circle of radius $10\text{m}$. Calculate angular displacement in radians & degrees.

1. $\frac{2\pi }{3}\text{rad},{120}^{\circ }$
2. $\frac{\pi }{3}\text{rad},{60}^{\circ }$
3. $\pi \text{rad},{180}^{\circ }$
4. $\frac{\pi }{4}\text{rad}.{45}^{\circ }$

Q. A spotlight is fixed $4\text{m}$ from the vertical wall and is rotating at a rate ${\text{1 rads}}^{-1}$. The spot moves vertically on the wall. Find the speed ( in ${\text{ms}}^{-1}$) of the spot on the wall when the spotlight makes an angle of ${45}^{\circ }$ with the wall.

Q. A car speeds up with constant magnitude of tangential acceleration in a circular path moving in anticlockwise direction. Which of the following figure best represents acceleration of the car?
वृत्ताकार पथ में वामावर्त दिशा में गतिशील एक कार नियत परिमाण के स्पर्शरेखीय त्वरण से अपनी चाल बढ़ाती है। निम्न में से कौनसा चित्र कार के त्वरण को सबसे सही रूप से प्रदर्शित करता है?

1. 
2. 
3. 
4. 

Q. A particle is rotating in a circle of radius $1\text{m}$ with constant speed $4\text{m/s}$. In time $1\text{s}$
$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ & \text{(Quantity)}& & \text{(Value in SI units)}\\ \text{(a)}& \text{Displacement}& \text{(p)}& 8\sin 2\\ \text{(b)}& \text{Distance}& \text{(q)}& 4\\ \text{(c)}& \text{Average velocity}& \text{(r)}& 2\sin 2\\ \text{(d)}& \text{Average acceleration}& \text{(s)}& 4\sin 2\end{array}$

1. a - r; b - p; c - q; d - s
2. a - r; b - q; c - p; d - s
3. a - r; b - p; c - r; d - s
4. a - r; b - q; c - r; d - p