Uniform Circular Motion

Question: A satellite rotate around the earth once time a day at a distance of 4.21 x 10^7 meters from the earth's center. Find the magnitude of acceleration felt by the satellite.

• The centripetal acceleration is given by ac = v^2 / r
• The speed is given by the circumference of the period, v= 2pi*r / T

r = 4.21 x 10^7, T =  one day = 86400 seconds

V = [2pi * (4.21 x 10^7) ] / 86400 = 3062 m/s

a = (3062)^2 / (4.21 x 10^7) = .223 m/s^2

Question: A race car weight 1500 kg is running at a speed of 45 m/s (100 mph) through a circular corner of the track. The radius of the circle path is 180 m. What is centripetal force exert toward the center of the track?

• Centripetal force is given by Fc = mac = (m*v^2 ) / r

     Fc = [1500 kg (45 m/s)^2] / 180 m

     = 16875 N