Circular Motion,Relative Motion And SHM

Question 1

Circular motion definition

Answer 1

When a particle moves in a plane such that it’s distance from a fixed(or moving) point remains constant, then it is said to be in circular motion with respect to that point.

Question 2

Position vector definition

Answer 2

A vector that establishes the position of a point in space relative to the arbitrary reference origin.

Question 3

Angular position of a point in space requires

Answer 3

An arbitrary origin and a reference line.

Question 4

Angular position of a point in space is defined as

Answer 4

The angle made by the position vector(w.r.t origin) with the reference line.

Question 5

Circular motion has …. dimensions

Answer 5

2

Question 6

2 types of acceleration in circular motion

Answer 6

Tangential acceleration

Centripetal acceleration

Question 7

Tangential acceleration direction

Answer 7

Tangential to the circular motion.

Question 8

Tangential acceleration changes the

Answer 8

Speed of the particle.

Question 9

Centripetal acceleration changes the

Answer 9

Direction of velocity

Question 10

Centripetal acceleration is also called

Answer 10

Radial acceleration or normal acceleration (R).

Question 11

Total acceleration (in circular motion)

Answer 11

Vector sum of tangential and centripetal acceleration (R).

Question 12

In circular motion there must be a

Answer 12

Force acting on the object otherwise, it should follow a linear motion.

Question 13

Motion definition

Answer 13

Change in position of an object over time.

W

Question 14

Relative position

Answer 14

Position of a particle with respect to the observer.

R

Question 15

The position of A w.r.t B is denoted by the

Answer 15

Displacement vector.
Position vector of A - Position vector of B.

And vice versa.

Question 16

Relative velocity of A with respect to B is

Answer 16

The velocity with which A appears to move, if B is at rest. (R)

Question 17

Periodic motion definition

Answer 17

When body repeats its motion along a definite path in regular intervals of time, it’s motion is said to be Periodic motion. (R)

Question 18

The regular intervals of time in which the periodic motion of an object repeats it

Answer 18

Time period or

Harmonic motion period (R)

Question 19

Time period definition

Answer 19

Smallest time interval after which the oscillation repeats itself. (R)

Question 20

Time period of a second pendulum

Answer 20

2 seconds. (R)

Question 21

Length of a second pendulum

Answer 21

.993 m.

Question 22

Angular displacement definition

Answer 22

Angle through which the position vector of a moving particle rotates in a given interval of time. (R)

Question 23

Angular displacement depends on

Answer 23

The origin ,but does not depend on the reference line. (R)

Question 24

Angle, Angular displacement, Angular velocity, Angular acceleration are all

Answer 24

Dimensionless quantities.

Question 25

1 rev =

Answer 25

360°

Question 26

1 revolution written as

Answer 26

1 rev

Question 27

Angular velocity is represented by

Answer 27

Omega

Question 28

Angular acceleration is represented by

Answer 28

Alpha

Question 29

Axial vectors definition

Answer 29

Vectors representing rotation effect. (R)

Question 30

If angular acceleration is 0 ,then circular motion is

Answer 30

Uniform.

Question 31

Angular acceleration acts along the

Answer 31

Axis of rotation

Question 32

Tangential acceleration acts

Answer 32

Tangentially to the circular path

Question 33

Tangential acceleration =

Answer 33

radius x angular acceleration

Question 34

Centripetal acceleration =

Answer 34

V*2/r

Question 35

Velocity of approach of 2 moving particles =

Answer 35

|V(ab)| = |V(ba)|

Question 36

V(ab)

Answer 36

Velocity of a with the respect to b, where b itself is considered to be at rest.

Question 37

Oscillatory motion

Answer 37

To and fro type of motion of objects

Question 38

Damped oscillations

Answer 38

Oscillations in which energy is consumed due to some resistive forces, thus causing the total mechanical energy to reduce.

Question 39

Restoring force

Answer 39

Force acting in an oscillation directed towards the equilibrium point.

Question 40

Simplest form of oscillatory motion

Answer 40

Simple Harmonic Motion

Question 41

Definition of SHM

Answer 41

If the restoring force acting on the body is directly proportional to the displacement of the body and is always directed towards the equilibrium position.

Question 42

Types of SHM

Answer 42

Linear SHM | Angular SHM

Question 43

In a linear SHM, the oscillation happens along a

Answer 43

Straight line.

Question 44

In an oscillation there is

Answer 44

2 extreme positions and 1 mean position(equilibrium point)

Question 45

Amplitude of a particle in SHM

Answer 45

Maximum value of displacement of a particle from its equilibrium position.

Question 46

Amplitude of a particle in SHM motion is directly proportional to the

Answer 46

Total mechanical energy of a body.

Question 47

Amplitude of a particle in SHM is quantitatively expressed as

Answer 47

A = 1/2 x (distance between the 2 extreme positions)

Question 48

For SHM to exist, only 1 condition is sufficient ?

Answer 48

F = -kx x : displacement k : spring constant

Question 49

Spring constant is also called as

Answer 49

Force constant.

Question 50

The linear displacement between 2 points in circular motion is

Answer 50

r∆θ

Question 51

s = rθ , prove it ?

Answer 51

S=(theta/2pi)(2pi*r)=r(theta)

Question 52

Proof of v = r ω v - linear speed r - radius ω - angular velocity

Answer 52

``` ∆s = r∆θ ∆s/∆t = r∆θ/∆t v = r ω ```

Question 53

Relationship btw angular velocity and linear velocity

Answer 53

v = r ω

Question 54

a(t) = r α | Derivation ?

Answer 54

By differentiating the equation v = r ω with respect to time.

Question 55

Tangential acceleration is the

Answer 55

Rate of change of speed and not velocity.

Question 56

In v = r ω, | v is

Answer 56

Linear speed and not linear velocity.

Question 57

Linear velocity vector is always

Answer 57

Tangential

Question 58

Linear speed =

Answer 58

Radius x angular velocity | v=r α

Question 59

Linear velocity

Answer 59

r ω [-i sinθ + j cosθ] = r ω e(t)

Question 60

Linear acceleration =

Answer 60

-ω²r e(r) + dv/dt e(t) e(r) and e(t) are unit vectors, with specific directions. e(r) : radial direction e(t) : tangential acceleration

Question 61

e(r) is the | [it was hard to put the arrow]

Answer 61

Radial unit vector = [i cosθ + j sinθ]

Question 62

e(t) is the | [it was hard to put the arrow]

Answer 62

Tangential unit vector = [-i sinθ + j cosθ]

Question 63

If it is uniform circular motion, then ..... is not present

Answer 63

Tangential acceleration

Question 64

Tangential acceleration =

Answer 64

dv/dt

Question 65

Resultant acceleration makes an angle alpha with the radius , and tan alpha =

Answer 65

(dv/dt)/(v²/r)

Question 66

Derivation of a(c) = v²/r from a(c) = ω²r

Answer 66

ω²r = (v²/r²) x r = v²/r

Question 67

Angular acceleration is a vector , but angular velocity is a

Answer 67

Scalar

Question 68

Angular displacement is

Answer 68

Scalar

Question 69

Angular displacement is a

Answer 69

Scalar, unless it is infinitesimally small.

Question 70

Distance travelled in n second

Answer 70

sn=u+a/2(2n-1)

Question 71

If the velocity of an object is less than √5gl then the motion of the particle depends on whether

Answer 71

The speed or tension will become 0 first.

Question 72

Conditions for speed to become 0 before tension

Answer 72

0 < velocity < √2gl | This happens only between 0° and 90°

Question 73

If the velocity is √2gl, then

Answer 73

The particle travels 90° and speed and tension becomes 0 at the same time.

Question 74

If speed becomes 0 before tension, then the object will

Answer 74

Oscillates

Question 75

Conditions for tension to become 0 first

Answer 75

√2gl < velocity < √5gl | This happens only between 90° and 180°

Question 76

If the object’s tension becomes 0 first, then the motion would be

Answer 76

A combined form of circular and projectile motion.

Question 77

Newton’s law are not valid in a

Answer 77

Non inertial frame.

Question 78

Centrifugal force is a

Answer 78

Pseudo force

Question 79

Pseudo forces have to be assumed if the frame in which we are working is

Answer 79

Non inertial

Question 80

Centrifugal force =

Answer 80

Centripetal Force = mv2/r

Question 81

If we analyse the motion of objects moving in a rotating frame many pseudo forces have to be assumed like

Answer 81

Coriolis Force,centrifugal Force etc.

Question 82

If we are working in an inertial frame

Answer 82

No pseudo forces have to be applied.

Question 83

Earth’s axis of rotation

Answer 83

Line joining North Pole and South Pole.

Question 84

Every point in earth

Answer 84

Moves in a circle

Question 85

Poles of the earth

Answer 85

Do not rotate and hence effect of earth’s rotation is not felt there.

Question 86

Relationship between mg and mg’ in poles and equator

Answer 86

In poles mg = mg’ In equator mg’ - mv*2/r = mg

Question 87

g’ ≥ g

Answer 87

T

Question 88

g’ =

Answer 88

g + mv²/r = √[g² − ω²Rsin²θ (2g-ω²r)]

Question 89

r =

Answer 89

R sin θ

Question 90

To convert Radians into degrees multiply it by

Answer 90

180/pie = 57.3

Question 91

Cos θ for very small angles (in Radians) can be found by

Answer 91

1-(θ²/2)