First slide

Angular velocity, Angular acceleration

Question

When the angular velocity of a uniformly rotating body has increased thrice, the resultant of forces applied to it increases by 60 N. Find the accelerations of the body in the two cases. The mass of the body m = 3 kg.

Moderate

A

$2.5 {ms}^{- 2}, 7.5 {ms}^{- 2}$
B

$7.5 {ms}^{- 2}, 22.5 {ms}^{- 2}$
C

$5 {ms}^{- 2}, 45 {ms}^{- 2}$
D

$2.5 {ms}^{- 2}, 22.5 {ms}^{- 2}$

Solution

F₁=M $ω^{2} R$ and F₂ = M (3 $ω$ )² R
given $∆ F = 9 F_{1} - F_{1} = 60 N$
SO a₁= $\frac{F_{1}}{M} = 2.5 m s^{- 2}$
a_{2 =} $\frac{F_{2}}{M} = 22.5 m s^{- 2}$

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