Question 460: Centre of Mass and Rotational Motion

Question

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

Accepted Answer

$${\omega _f} = 2460 	imes {{2\pi } \over {60}}$$
$$ = 82\pi $$
$${\omega _i} = {{900 	imes 2\pi } \over {60}} = 30\pi $$
$$\alpha  = {{{\omega _f} - {\omega _i}} \over t}$$
$$ = {{82\pi  - 30\pi } \over {26}}$$
= 2 $$\pi$$ rad/sec
2
$$	heta  = {{\omega _f^2 - \omega _i^2} \over {2\alpha }}$$
$$ = {{(82\pi  + 30\pi )(82\pi  - 30\pi )} \over {2 	imes 2\pi }}$$
$$ = {{(112 	imes 52){\pi ^2}} \over {4\pi }}$$
No. of revolution $$ = {{(112 	imes 13)\pi } \over {2\pi }}$$
= 728

Centre of Mass and Rotational Motion

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

Integer / Numeric Answer Type