circular motion

Question 1

angular displacement

Answer 1

It is defined as the angle turned by the particle from some reference line. Angular
displacement ∆θ is usually measured in radians.

Question 2

angular velocity

Answer 2

Angular velocity, ω=(dθ/dt)

It is an axial vector whose direction is given by the right hand rule. Its unit is rad/s

Question 3

angular acceleration

Answer 3

It is the rate of change of angular velocity.
α=dω/dt=d^2θ/dt^2
ts unit is rad/s^2

Question 4

dynamics of uniform circular motion

Answer 4

dv/dt=0 Ac=ω^R=v^2/r towards the center. This

acceleration is termed as centripetal acceleration.

Question 5

in a non-uniform circular motion resultant acceleration

of the body

Answer 5

a==√(a_r^2+a_T^2 )=√(v^4/r^2 +r^2 α^2 )

Question 6

centripetal forces

Answer 6

centripetal force is along the radius, acting towards the centre
of the circle, on which the given body is moving.
Centripetal force,
F=(mv^2)/r=mrω^2=mr4π^2 v^2=mI (4π^2)/T^2
Work done by centripetal force is always zero

Question 7

centrifugal force

Answer 7

Certrifugal force can be defined as the radially directed outward force
centrifugal force =Mv^2/r=mrw^2

Question 8

motion of a vehicle on a level circular road

Answer 8

. Thus, for maintaining its circular
path required centripetal force
((mv^2)/r)≤" frictional force "(μmg)
Maximum speed v_max=√μrg
where, µ = coefficient of friction between road and vehicle
tyres and r = radius of circular path.

Question 9

bending of a cyclist

Answer 9

When a cyclist goes round turns in a circular track, then angle
made by cyclist with vertical level is given by
■(tan⁡θ =v^2/rg≈θ=tan^(-1)⁡(v^2/rg) )

Question 10

banking of curved road

Answer 10

Let the road be banked at an angle θ from the horizontal
If b is width of the road and h is height of the outer edge of the road as compared to the inner edge,

tanθ=v^2/rg=h/b
V_max=√(rg(μ_s+tan⁡θ)/(1-μ_s tan⁡θ))
μ_s= coefficient of static friction.