Let's say we have a merry-go-round with a radius of 3.00m, a period of 4.00 seconds and a child that's 30.0kg.
How to calculate Linear Speed:
V= distance/time = circumference/time ..soo.. V=(2*pi*r)/time
V= (2*pi*3m)/4sec
V ~ 4.71m/s
How to calculate Acceleration:
a= (v^2)/r = (4*pi^2)r/T^2
= (4.71m/sec)^2/3m or = (4*pi^2)(3m)/(4.00sec)^2
~ 7.39m/sec^2 ~7.40m/sec^2
very close!!
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All equations are thanks to Matthew
Hutchins!! With changes in variables ;)
http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.htmlHow to calculate
Angular Speed:
ẘ = (2*pi)/T .. = 2*pi*frequency = v/r
= (2*pi)/4.00sec =4.71m/s / 3.00m
~1.57rad/sec ~1.57rad/sec
ẘ = (2*pi)/T .. = 2*pi*frequency = v/r
= (2*pi)/4.00sec =4.71m/s / 3.00m
~1.57rad/sec ~1.57rad/sec