1. An ant is riding in a car while sitting on a rotating compact disc. The car i

Question

1. An ant is riding in a car while sitting on a rotating compact disc. The car is moving at a steady velocity of 30 m/s in the x-direction and the compact disc is 10 cm in diameter and rotating in circular motion at a constant rate of 10 revolutions per sec.

i. Write a vector describing the motion of (just) the car.

ii. Write a vector describing the ant riding on the compact disc when the car is stopped.

iii. Combine the two vectors to write a displacement vector for the ant riding on a compact disc in the moving car as a function of time (assume at t=0 the ant is at x=0, y =0

iv. Calculate the velocity of the ant on the compact disc in a moving car as a function of time.

v. Calculate the speed of the ant on the compact disc in the moving car at time t = 0.

vi. Calculate the acceleration vector of the ant at t = 0.

Explanation / Answer

i cap is unit vector along +ve x-axis and j cap is unit vector along +y axis

I.

Vcar = 30i m/s

II.
angular velcoity of disc w = 10 rev/sec = 10 x 2pi rad /s

w = 125.66 rad/s

tangential velocity = w.r = 125.66 x 0.10 = 12.6 m/s

VdueDisc = 12.6 j m/s

III.
Displacement = velocity x time ( velocity is constant )

r = 30t i + 12.6t j

IV.

velocity is constant (independent of time)

v = 30i + 12.6j m/s

V.
speed =sqrt(30^2 + 12.6^2 ) = 32.54 m/s

VI.

there is only centripetal acc. due to rotation.
a = w^2 r (-i)

a = - 125.6^2 x 0.10 = - 1577.54i m/s^2

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