Question

A 210 g toy car is placed on a narrow 70-cm-diameter track with wheel grooves that keep the car going in a circle. The 1.1 kg track is free to turn on a frictionless, vertical axis. The spokes have negligible mass. After the car's switch is turned on, it soon reaches a steady speed of 0.71 m/s relative to the track

What then is the track's angular velocity, in rpm?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Anngular momentum of the car, Lc = Ic_c
Ic = mR², _c = v/R
Where m is the mass ot the car, v is the velocity and R is the radius of rotation
Lc = [mR²] x v/R
= mvR
= 0.210 x 0.71 x 0.35
= 0.052185 kg m²/s

Angular momentum of the track, Lt = It_t
It = MR²= 1.1 x (0.35)²
= 0.13475 kgm2

Using conservation of angular momentum,
Lc = Lt
0.052185 = 0.13475 x _t
t = 0.382 rad/s
1 rev = 2 rad,
1 rad = 1/2 rev
0.382 rad/s = 0.382/2 rev/s = 0.062 rev/s
= 0.062 x (60/60) rad/s = 0.062 x 60 rpm
= 3.698 rpm