Question

You would feel weightless at the equator on this planet, if it rotated fast enough so that the centripetal acceleration at the planet's surface was equal to the acceleration due to gravity (which in this case is 11.4 m/s2). calculate the new rotational period for this planet necessary to produce this effect! calculate the period in hours. enter only the numerical value--no units necessary.

Answer 1

To calculate the new rotational period necessary for a planet to produce weightlessness at the equator, use the centripetal acceleration formula, solve for the linear velocity, and then calculate the period using the planet's radius and the velocity. Convert this value into hours for the final answer.

Step-by-step explanation:

To calculate the new rotational period for a planet, where the centripetal acceleration is equal to the planet's gravitational acceleration, we use the formula for centripetal acceleration ac = v2 / r, where v is the linear velocity and r is the radius. If ac becomes equal to the gravitational acceleration g (given as 11.4 m/s2), then we have v2 / r = g. Solving for v, we get v = √(gr). Knowing the linear velocity, we can find the rotational period T by using the relationship T = 2πr / v. Converting this period from seconds to hours is done by dividing by 3600 (the number of seconds in an hour).

To provide an actual numerical value, we would need the planet's radius r, which is not given in the problem statement. However, assuming the radius is known, the steps outlined above would be followed to calculate the exact rotational period in hours.