Algebra 2 HW Help

Question

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular velocity? How far will it travel in that time? Round to the nearest tenth.

 

1,800°; 9 rev/sec

 

The coin will take approximately ___ sec to roll 1,800° and travels approximately mm.

Answer 1

To find the time it took the coin to spin 1800 degree is a matter of unit conversion:

(1800°) × (1 rev / 360°) × (1 s / 9 rev) ≅ .56 s

Then to find the distance traveled use the physics equation angular vel. equals(ω) = tangential vel. (v) / radius in order to solve for the coins speed.

ω = v / radius

v = ω × radius

= 9 rad/sec × 10 mm

= 90 mm/sec

And lastly solve for the distance with the equation d = v × t, to get the answer of 50.4 mm traveled by the coin over the .56 seconds it took the coin to rotate 1800°.