Question

(A) How do you explain that an object is in uniform circular motion
(B) Calculate the acceleration of the moon towards earth's center.

Answer 1

(a) An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards.

(b) Separation between earth and moon is $384.4\times {10}^6$ meter.

Centripetal force = force of attraction

$\frac{m{v}^2}{r}=\frac{G{M}_{e}m}{r^2}$

Centripetal acceleration = $\frac{v^2}{r}=\frac{G{M}_e}{r^2}=\frac{6.67\times {10}^{-11}\times 5.97\times {10}^{24}}{{(384.4\times {10}^6)}^2}=2.69\times {10}^{-3}m{s}^{-2}$

Hence, acceleration toward earth is $2.69\times {10}^{-3}m{s}^{-2}$