Question

for a body in circular motion with constant angular velocity,the magnitude of average acceleration over a period of a half of revolution is... times the magnitude of instantaneous acceleration

Answer 1

hope u understand the calculations yourself

Answer 2

Explanation:

According to classical rotational mechanics,  

Instantaneous acceleration $=\frac{v^{2}}{r}$

Average acceleration $=\frac{\text { change in velocity }}{\text { change in time }}$

Now an object in uniform rotation has the same speed throughout but there is a change in the direction by 180°. Hence if we consider the initial velocity as v, the final velocity after half rotation is equal to -v.

So, change is $\frac{v-(-v)}{t}=\frac{2 v}{t}$

T= distance travelled / velocity

Distance travelled = πr

So, average acceleration $=\frac{2 \pi v^{2}}{r}=2 \pi x$ instantaneous acceleration.