Question

264 fps ·チ 3 0

Answer 1

Circumference of bigger wheel:

$\pi$D = $\pi$ x 9 = 28.27 inch = 2.35 ft

Circumference of smaller wheel:

$\pi$D = $\pi$ x 6 = 18.84 inch = 1.57 ft

Velocity of lawn mover = 264 fps

RPM of wheels:

Velocity of lawn mover / Circumference of wheel

Therefore, 264 / 2.35 = 112.34 rps = 6740.4 rpm

Similarly for smaller wheel,

264 / 1.57 = 168.15 rps = 10089.17 rpm

Angular velocity of the wheels

Bigger wheel: Angular velocity = RPM x 6

= 6740.4 x 6

= 40442.4 rad/sec

Smaller wheel: Angular velocity = RPM x 6

= 40089.17 x 6

= 240535.02 rad/sec

tangential velocity formula:

V = r x $\omega$

Bigger wheel: V = 4.5 x 40442.4

= 181990.8 inch/sec

V = 4622.5 m/sec

Smaller wheel:   V = 3 x 240535.02

= 721605.06 inch/sec

V = 18328.7 m/sec

Hence,

V_A = V_B = 4622.5 m/sec ------------ (Point A and B are on the same wheel)

V_C = 18328.7 m/sec