A record player is spinning at an angular velocity of 45 ~rpm just before it is turned off. It then decelerates at a constant rate of 0.8 ~rad ~s ⁻¹ . The angular displacement is

Step-by-step solution

The initial angular velocity ₀ is given as 45 rpm . Converting this to rad s ⁻¹ : ₀ = 45 2 60 rad s ⁻¹ = 45 2 60 rad s ⁻¹ = 1.5 rad s ⁻¹ 4.712 rad s ⁻¹ . The deceleration is 0.8 rad s ⁻² . Since it is decelerating, = -0.8 rad s ⁻² . The final angular velocity when the record player stops is 0 rad s ⁻¹ . Using the kinematic equation ^2 = ₀^2 + 2 , where is the angular displacement: 0 = (1.5 )^2 + 2(-0.8) 1.6 = (1.5 )^2 1.6 = 2.25 ^2 Taking ^2 9.8696 : 1.6 = 2.25 9.8696 = 22.2066 = 22.2066 1.6 = 13.879 rad 13.88 rad