# Angular Displacement

## Trending Questions

**Q.**A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is

- 1 cm
- 9 cm
- 3 cm
- 27 cm

**Q.**A wheel starts from the rest and attains an angular velocity of 20 rad/s after being uniformly accelerated for 10 s. The total angle in radians through which it has turned in 10 s is

- 20
- 40
- 80
- 100

**Q.**A uniform cylinder of height h and radius r is placed with its circular face on a rough inclined plane and the inclination of the plane to the horizontal is gradually increased. If μ is the coefficient of friction, then under what condition the cylinder will slide before toppling.

- μ<2rh

- μ>2rh

- μ<rh

- μ>rh

**Q.**The minimum and maximum distances of a planet revolving around sun are r and R. If the minimum speed of planet on its trajectory is v0, its maximum speed will be

- v0Rr
- v0rR
- v0R2r2
- v0r2R2

**Q.**

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.

**Q.**A wheel starting from rest, rotates with a uniform angular acceleration of 2 rad/s2. The number of rotation it performs in the tenth second is

- 3
- 6
- 9
- 12

**Q.**A balloon is moving upwards with a speed of 20 m/s. When it is at a height of 14 m from the ground in front of a plane mirror as shown in figure, a boy drops himself from the balloon. Find the time duration for which he will see the image of source S placed symmetrically before the plane mirror during free fall. Take g=10 m/s2.

- 4.5 s
- 3.7 s
- 1.7 s
- 2.7 s

**Q.**A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle θ1 in the first 2s. In the next 2 s, it rotates through an additional angle θ2, the ratio of θ2θ1 is

- 1
- 2
- 3
- 4

**Q.**A particle is rotating in a circle of radius 1 m with constant speed 4 m/s. In time 1 s

Column - I Column - II (Quantity)(Value in SI units)(a)Displacement(p)8sin2(b)Distance(q)4(c)Average velocity(r)2sin2(d)Average acceleration(s)4sin2

- a - r; b - p; c - q; d - s
- a - r; b - q; c - p; d - s
- a - r; b - p; c - r; d - s
- a - r; b - q; c - r; d - p

**Q.**

Find the angular velocity of a body rotating with an acceleration of 2 rev/s2 as it completes the 5th revolution after the start.

**Q.**An opaque sphere of radius a is just immersed in a transparent liquid as shown in figure. A point source is placed on the vertical diameter of the sphere at a distance a2 from the top of the sphere. A ray from the point source after refraction from the air liquid interface forms tangent to the sphere. The angle of refraction for that particular ray is 30∘. The refractive index of the liquid is

- 2√3
- 3√5
- 4√5
- 4√7

**Q.**

A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.

**Q.**

A capillary tube of radius 1 mm is kept vertical with the lower end in water . (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part (a), find the angle θ made by the water surface in the capillary with the wall.

**Q.**

A bird is flying up at angle sin−1(3/5) with the horizontal. A fish in a pond looks at that bird. When it is vertically above the fish, the angle (in degrees) at which the bird appears to fly (to the fish) is [nwater=4/3]

**Q.**Find the angular displacement of the hour hand of a normal clock in 4 h

- π3
- π6
- 2π3
- 3π2

**Q.**If an object covers a distance of 5 cm moving in a circular path of radius 5 cm, find its angular displacement in radians.

- 1
- 0
- 5
- 25

**Q.**The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t)=3t3−9t2 (Here t is in seconds). The angular acceleration of the wheel becomes zero at

- t=1 s
- t=0.5 s
- t=0.25 s
- t=2 s

**Q.**A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

- 20 rad
- 30 rad
- 15 rad
- 7.5 rad

**Q.**Neena goes around a circular track that has a diameter of 7 m. If she runs around the entire track for a distance of 50 m, what is her angular displacement?

- 6.28 radians
- 3.14 radians
- 7.14 radians
- 14.28 radians

**Q.**Why is angular displacement vector quantity only for small values? Why is the direction of angular displacement perpendicular to the plane of rotation of object?

**Q.**A boy running on a circular track of radius 10 m completes 3 revolution and comes back to the point from where he started. Calculate the angular displacement of the boy (in rad).

- 3π
- 6π
- π3
- 0

**Q.**

Give an example of variable velocity when the magnitude is constant and the direction is changing.

**Q.**An athlete running with constant speed, completes one round of a circular track of radius R in 40 seconds. What will be his angular displacement at the end of 20 seconds?

- π2 rad
- π3 rad
- π4 rad
- π rad

**Q.**A spotlight is fixed 4 m from the vertical wall and is rotating at a rate 1 rads−1. The spot moves vertically on the wall. Find the speed ( in ms−1) of the spot on the wall when the spotlight makes an angle of 45∘ with the wall.

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

**Q.**A particle is moving in a circle of radius R with initial speed v. It starts retarding with constant retardation v24πR. The number of the revolution it makes in time 8πRv is

- 3
- 4
- 5
- 2

**Q.**

A point initially at rest moves along $X-axis$. Its acceleration varies with time as $a=(6t+5)m{s}^{-2}$. If it starts from origin, the distance covered in $2s$ is

$20m$

$18m$

$16m$

$25m$

**Q.**

Derive the second equation of motion.

**Q.**When a wheel completes 2000 revolutions to cover 15 km distance, then the radius of the wheel is?

- 2.4 m
- 2 m
- 1.19 m
- 0.8 m

**Q.**why infinitesimal angular displacement is a vector rather avg angular displacement or velocity a scalar ?!!!