Acylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s 2 starts from rest at t = 0. at the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

a = 0.27 rad/s^2

Explanation:

First we will find the time t using the next equation:

θ =

where θ is the angle in radians and a is the angular aceleration. So:

0.4 =

Solving for t:

t = 0.707s

Second, with that time, we will find the angular velocity w using the next equation:

w = at

where a is the angular aceleration, so:

w = (1.6)(0.707s)

w = 1.1312 rad/s

Now, the radial aceleration is calcualted as:

=

=

= 0.166 rad/s^2

Additionally, the tangential aceleration is calculated as::

Finally, by pythagoras theorem, we find the total linear acceleration as:

a = 0.27 rad/s^2

current flows in a wire

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min