Question

1. A certain CD has a playing time of 74 minutes. When the music starts, the CD is rotating at an angular speed of 4.70×10(2) revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.40×10(2) rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s².
2.The pedals of a bicycle rotate in a circle with a diameter of 40 cm. What is the maximum torque a 64-kilogram rider can apply by putting all of her weight on one pedal?

Answer 1

1.

Answer:

$\alpha = -5.42 \times 10^{-3} rad/s^2$

Explanation:

Initial angular speed of the CD is given as

$\omega_i = 2\pi f_i$

$\omega_i = 2\pi(\frac{4.70 \times 10^2}{60})$

$\omega_i = 49.2 rad/s$

Similarly final angular speed is given as

$\omega_f = 2\pi f_f$

$\omega_f = 2\pi(\frac{2.40 \times 10^2}{60})$

$\omega_f = 25.13 rad/s$

now angular acceleration is given as

$\alpha = \frac{\omega_f - \omega_i}{t}$

$\alpha = \frac{25.13 - 49.2}{74 \times 60}$

$\alpha = -5.42 \times 10^{-3} rad/s^2$

2.

Answer:

$\tau = 125.57 Nm$

Explanation:

As we know that torque is the product of force and its distance from the axis of rotation

so we will have

$\tau = r \times F$

so we have

$F = mg$

$F = (64 \times 9.81)$

now we have

$\tau = (64 \times 9.81)(0.20)$

$\tau = 125.57 Nm$