Question 40: Centre of Mass and Rotational Motion

Question

A solid cylinder of mass $2 \mathrm{~kg}$ and radius $0.2 \mathrm{~m}$ is rotating about its own axis without friction with angular velocity $5 \mathrm{~rad} \mathrm{s}^{-1}$. A particle of mass $1 \mathrm{~kg}$ moving with a velocity of $5 \mathrm{~ms}^{-1}$ strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lwwyl0rw/de6bf2bc-8ec2-42fd-b51e-dfeefb261299/ddd886c0-208c-11ef-9350-af9c1c651b06/file-1lwwyl0rx.png?format=png)

Accepted Answer

The correct answer is
Option C: Angular momentum
. Here's why:
Let's break down the units and their relationships:
Joule (J):
The unit of energy.  Energy is the capacity to do work.
Second (s):
The unit of time.
Angular Momentum (L):
A measure of an object's rotational inertia. It's calculated as the product of the object's moment of inertia (I) and its angular velocity (ÃÂ):
$L = IÃÂ$
Now, let's look at the units involved in angular momentum:
Moment of Inertia (I):
Measured in kilogram-meter squared (kgÃÂ·mÃÂ²)
Angular Velocity (ÃÂ):
Measured in radians per second (rad/s)
Combining these, the units of angular momentum are:
$L = IÃÂ = (kgÃÂ·mÃÂ²) (rad/s) = kgÃÂ·mÃÂ²/s$
Since radians are dimensionless, we can simplify this to
kgÃÂ·mÃÂ²/s
.  Notice that this is equivalent to
Joule-second (JÃÂ·s)
.
Therefore, Joule-second (JÃÂ·s) is the unit of
angular momentum
.
Let's address why the other options are incorrect:
Option A: Energy
- Energy is measured in Joules (J), not Joule-seconds (JÃÂ·s).
Option B: Power
- Power is the rate at which energy is transferred, measured in Watts (W), which is equivalent to Joules per second (J/s).
Option D: Linear momentum
- Linear momentum is a measure of an object's mass in motion. It's calculated as the product of the object's mass (m) and its velocity (v):
$p = mv$
Linear momentum is measured in kilogram-meters per second (kgÃÂ·m/s).

Answer

$
15.0 \mathrm{~rad~s}^{-1}
$

Answer

$
12.0 \mathrm{~rad~s}^{-1}
$

Answer

$
10.0 \mathrm{~rad~s}^{-1}
$

Answer

$
30.0 \mathrm{~rad~s}^{-1}
$

Centre of Mass and Rotational Motion

Choose the correct answer: