Question

If an object moves in uniform circular motion in a circle of radius R = 2.00 meters, and the object takes 5.00 seconds to complete ten revolutions, calculate the centripetal acceleration. ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements. a= _____ m/s2 39.4 m/s 2 100. m/s 2 158 m/s 2 50.2 m/s 2

Answer 1

The centripetal acceleration of the object is approximately 39.4 m/s^2.

Step-by-step explanation:

To calculate the centripetal acceleration, we can use the formula ac = (v^2) / r, where ac is the centripetal acceleration, v is the linear velocity, and r is the radius of the circle. First, let's find the linear velocity. Since the object takes 5.00 seconds to complete ten revolutions, we can calculate the angular velocity using the formula w = (2*π*n) / t, where w is the angular velocity, n is the number of revolutions, and t is the time taken. Substituting the given values, we have w = (2*π*10) / 5 = 4*π rad/s. Now, we can find the linear velocity using the formula v = r*w, where v is the linear velocity and r is the radius of the circle. Substituting the given values, we have v = 2*π*4*π = 8*π^2 m/s. Plugging in the values into the formula for centripetal acceleration, we have ac = (8*π^2)^2 / 2.00. Calculating this expression, we get ac ≈ 39.4 m/s^2.