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 * 10^(-3) rad/s^2`

Step-by-step explanation:

Initial angular speed of the CD is given as

`\omega_i = 2\pi f_i`

`\omega_i = 2\pi((4.70 * 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((2.40 * 10^2)/(60))`

`\omega_f = 25.13 rad/s`

now angular acceleration is given as

`\alpha = (\omega_f - \omega_i)/(t)`

`\alpha = (25.13 - 49.2)/(74 * 60)`

`\alpha = -5.42 * 10^(-3) rad/s^2`

2.

Answer:

`\tau = 125.57 Nm`

Step-by-step 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 * F`

so we have

`F = mg`

`F = (64 * 9.81)`

now we have

`\tau = (64 * 9.81)(0.20)`

`\tau = 125.57 Nm`