Question

A rod of length L fixed at the origin at one end is placed along the x-axis at t = 0. It starts rotating about the z-axis in the x-y plane anti-clockwise as seen from the positive z-axis. The angular displacement is given by θ = 2t2. The angular acceleration of the rod is 
1. 1 rad/s²
2. 2 rad/s2
3. 3 rad/s2
4. 4 rad/s2

Answer 1

Correct Answer - Option 4 : 4 rad/s2

CONCEPT:

Kinematic equations of rotational motion about a fixed axis,

\(\Rightarrow ω = \frac {d θ}{dt}\)

\(\Rightarrow α= \frac {d ω}{dt}\)

\(\Rightarrow α= ω \frac {d ω}{d θ}\)

where ω is the instantaneous angular velocity, α is the instantaneous angular acceleration, θ is the angular displacement, and t is time.

EXPLANATION:

Given: Length of the rod = L, and angular displacement θ = 2t2

• Using the first equation, 

\(\Rightarrow ω = \frac {d θ}{dt}\)

\(\Rightarrow ω = \frac {d (2t^2)}{dt} = 4t\)

• Using the second equation, 

\(\Rightarrow α= \frac {d ω}{dt}\)

\(\Rightarrow α= \frac {d (4t)}{dt} = 4 \space rad/s^2\)

• Therefore option 4 is correct.