Question

What is the angular acceleration of a ball that starts at rest and increases its angular
velocity uniformly to 5 rad/s in 10 s?​

Answer 1

Given :

A ball starts at rest and gained an angular velocity of 5 rad/sec in 10 s.

initial angular velocity (ω) = 0 rad/sec

Final angular velocity (ω') = 5 rad/sec

time (t) = 10 sec

To Find :

Angular acceleration ($\alpha$) of the ball

Solution :

We know, when a body travels with a uniform angular acceleration,

                      ω' = ω + $\alpha$t

or,                  5  = 0  +  $\alpha$ x 10

∴                   $\alpha$   =  $\frac{5}{10}$ = 0.5 rad/sec²  

Angular acceleration of the ball after 10 s is 0.5 rad/sec².  

 

Answer 2

Given:

Angular velocity (ω) = 5 rad/s

Time (t) = 10 s

To find:

Angular acceleration of the ball $(\alpha ).$

Solution:

• Angular acceleration of a rotating body is the acceleration equivalent used in linear motion.

• Mathematically, angular acceleration is the change in angular velocity with respect to time.

                        Angular acceleration $\alpha = \frac{dw}{dt}$  

According to the question, we have been given that the ball starts from rest and gains an angular velocity of $5 rad/s$ in $10s$.

Therefore, We have

$w_{0}=0rad/s$    $;$  $w_{t} = 5rad/s$    $;$  $t=10s$

Substituting in the given equation,we get

$\alpha =\frac{5-0}{10}$

$\alpha = 5rad/s^{2}$

Final answer:

Hence, the angular acceleration of the ball will be $5rad/s^{2}$.