An ant is riding in a car while sitting on a rotating compact disc. The car is m
ID: 1772408 • Letter: A
Question
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.
1. Write a vector describing the motion of (just) the car.
2. Write a vector describing the ant riding on the compact disc when the car is
stopped.
3. 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
4. Calculate the velocity of the ant on the compact disc in a moving car as a
function of time.
5. Calculate the speed of the ant on the compact disc in the moving car at time t = 0.
6. Calculate the acceleration vector of the ant at t = 0.
Explanation / Answer
i cap is unit vector along +ve x-axis
j cap is unit vector along +y axis
1.
Vcar = 30i m/s
2.
angular velcoity of disc w = 10 rev/sec = 10 * 2pi rad /s
w = 125.66 rad/s
tangential velocity = w.r = 125.66 * 0.10 = 12.6 m/s
VdueDisc = 12.6 j m/s
3.
Displacement = velocity * time
r = 30t i + 12.6t j
4.
velocity is constant (independent of time)
v = 30i + 12.6j m/s
5.
speed =sqrt(30^2 + 12.6^2 )
Calculate
=32.54 m/s
6.
there is only centripetal acc. due to rotation.
a = w^2 r (-i)
Put value
a = - 125.6^2 * 0.10 = - 1577.54i m/s^2