Test: Kinematics of Rotational Motion - JEE MCQ

Unlike linear motion, where velocity and acceleration are directed along the line of motion, in circular motion the direction of velocity is always tangent to the circle. This means that as the object moves in a circle, the direction of the velocity is always changing. A linear velocity of a particle performing circular motion, which is directed along the tangent to the circular path at given point on the circular path at that instant is called instantaneous velocity. It is also called as tangential velocity.

Given,
Angular velocity of the hour hand-H
Earth’s speed around its own axis-E
So, time taken by hour hand to complete a rotation is=T_H=12hr
Time taken by earth to complete a rotation =T_E=24 hours
So,
ω_E/ω_H =(2π/T_E )/2π/T_H=T_H/T_E=1/2
⇒ ω_E/ω_H=1/2
⇒ 2 ω_E= ω_H

The answer is option A
So, as we know,
After differentiating angular velocity with respect to t,
Linear velocity=2t+2.3=ω
Now,
Velocity=r x ω(where r is 0.8m)
=0.8x2.3
=1.84m/s

Thus, it is the velocity of a reference point fixed to the body. During purely translational motion (motion with no rotation), all points on a rigid body move with the same velocity. However, when motion involves rotation, the instantaneous velocity of any two points on the body will generally not be the same.

Clock wise direction means inward field so angular velocity is negative. Anticlockwise means outward field so angular velocity is positive.

Angular displacement is measured in units of radians. 2 pi radians equals 360 degrees. The angular displacement is not a length (i.e. not measured in meters or feet), so an angular displacement is different than a linear displacement.

Axis is along AD so Moment of inertia of first mass is zero and 2nd and 3rd masses are at distance of 6/2 from axis, so by using simply I=mr² we get, I=60×36/4+60×36/4=1080 g cm²

The correct option is A

2.6 rad/ s²

r=0.5m, t=15s
n₁=5rpm=5/60 rps
n₂=25rpm=25/60rps
… ω₁=2π(5) rad/s
… ω₂=2π(25) rad/s
As,
a=r∝          [∝=ω₂- ω₁/t]
so, a=0.5[2π(n₂-n₁)/t]
a=0.5x6.28x20/60x15
a=6.28x2/60x3
a=6.28/90
a=0.697 m/s²
a≈0.7 m/s²

F = w/2π
w = 2πf
w = 2π × 10
w = 62.8
L = Iw
I = L/w
I = 31.4/62.8
I = 0.5 kgm2
Hence A

First we have to find ‘v’ by using the relation v = rw
Now, v = 0.167m/s
Then we find ‘a’ by using the relation a = v/t
So, a = 0.0152m/s².
Now, we can find angular acceleration by using the formula α = a/r
Finally, α = 0.0076 rad/sec²

The equation τ = mr2α is the rotational analog of Newton's second law (F=ma), where torque is analogous to force, angular acceleration is analogous to translational acceleration, and mr2 is analogous to mass (or inertia).

Time taken to complete one rotation is 60 seconds.
One rotation involves 360 degree = 2π
Formula of angular velocity = theta/time taken
Hence, omega = 2π/60
= π/30 rad/s

So, “I” gets cancelled.