Physics: An lp turntable must spin at 3.500 rad/s to play a record. how much torque must the motor deliver if the turntable is to reach its final angular speed in 1.800 revolutions, starting from rest? the turntable is a uniform disk of diameter 30.80 cm and mass 0.2500 kg.

An lp turntable must spin at 3.500 rad/s to play

Ответ:

deena7

15.01.2022

Physics

0.00321 Nm

Explanation:

$\omega_f$ = Final angular velocity = 3.5 rad/s

$\omega_i$ = Initial angular velocity = 0

$\alpha$ = Angular acceleration

$\theta$ = Angle of rotation = 2 rev

Equation of rotational motion

$\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \alpha=\frac{\omega_f^2-\omega_i^2}{2\theta}\\\Rightarrow \alpha=\frac{3.5^2-0^2}{2\times 2\pi \times 1.8}\\\Rightarrow \alpha=0.54156\ rad/s^2$

Moment of inertia is given by

$I=mr^2\\\Rightarrow I=0.25\times 0.154^2\\\Rightarrow I=0.005929\ kgm^2$

Torque is given by

$\tau=I\alpha\\\Rightarrow \tau=0.005929\times 0.54156\\\Rightarrow \tau=0.00321\ Nm$

The torque required is 0.00321 Nm

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Ответ:

kortlen4808

05.02.2022

Physics

The mechanical energy in this case is the sum of the kinetic energy (KE) and the potential energy (PE). Below are the equations used for solving as well as the substitution.
KE = 0.5mv² = 0.5(2 kg)(1 m/s)² = 1 kg m²/s² = 1 J
PE = mgh = (2 kg)(9.8 m/s²)(0.5 m) = 9.8 kg m²/s² = 9.8 J
The sum of the two energies is the mechanical energy,
ME = KE + PE = 1 J + 9.8 J = 10.8 J
Therefore, the answer is the second choice.

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An lp turntable must spin at 3.500 rad/s to play a record. how much torque must the motor deliver if the turntable is to reach its final angular speed in 1.800 revolutions, starting from rest? the turntable is a uniform disk of diameter 30.80 cm and mass 0.2500 kg.

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