Rotational Motion Question

Question

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest and experiences angular acceleration of 2.0 rad/s^2 for 2.0 seconds. During this motion, consider the spider at the edge of the disk. Which statement is TRUE?

a) The tangential acceleration of the spider is 2.0 m/s^2.

b) The centripetal acceleration of the spider is constant throughout the motion.

c) The tangential acceleration of the spider is proportional to the angular acceleration.

d) The centripetal acceleration of the spider is always less than its tangential acceleration.

Answer 1

V = Rw

So a = R * Angular acceleration

Linear acceration = a = R * 20 = 0.1 * 20 = 2 m/s2

a is Correct

Cenrtripetal acceleration = V²/R

As Linear velocity is increasing , Centripetal acceleration also increases

b is not correct

a= R*Angular acceleration

c is correct

a= 0.1* Angular acceleration

d is also true