Question

A torque of 1 N-m is applied to a wheel which is at rest. After 2 seconds the angular momentum in $kg/{m^2}/s$ is?

Answer 1

Hint: Torque is defined as the change in angular momentum in unit time. Torque is the angular force required to rotate an object. Angular momentum is also known as rotational momentum, it is proportional to mass, linear velocity and perpendicular radius. Here we are given the value of torque (1N-m) and time (2s). Put the given value of torque and time in the equation that relates torque and angular momentum.


Formula Used:
The formula that relates torque and angular momentum is given by:
$\dfrac{{dL}}{{dt}} = \tau $
Where:
L = Angular Momentum
t = Time
$\tau $= Torque

Complete step by step answer:
Given:
$\tau $= 1N-m;
t = 2s
Find:
Angular momentum

Put the given values in the equation:
$\dfrac{{dL}}{{dt}} = \tau $
$\dfrac{{(L - 0)}}{{(t - 0)}} = \tau $
Initial time and initial angular momentum is zero.
$\dfrac{L}{t} = \tau $
Put values of t and $\tau $
$\dfrac{L}{2} = 1$
Solve,
$L = 2kg{m^2}/s$
Final Answer: The angular momentum is $L = 2kg{m^2}/s$

Additional Information: Just like force torque is known as angular force. There are two types of torque one is static torque and another one is dynamic torque. Static torque does not cause rotational motion while dynamic torque does. The formula for torque is given as $\tau = F.r\sin \theta $, where $\tau $= torque, F= Force, r= distance. Angular momentum is defined as the product of two quantities namely moment of inertia and angular velocity. Here moment of inertia is the body opposition or resistance to a rotational motion. Angular velocity is defined as how fast an object rotates or revolves. Formula for angular momentum is $L = mvr$. Where L= Angular momentum, m= mass, v= velocity, r= radius.

Note: Here make sure to describe torque and angular momentum. Establish a proper relation between the two and find out the angular momentum form the given values of torque and time. Be careful while writing the unit of angular momentum.