Question

2. 17.42 A disc drive is driven by a friction driver, as shown in Fig. P17.42. Initially, the angular velocity of the disc is $ \omega_2 $ [rad/s], clockwise, and that of the driver is $ \omega_1 $ [rad/s], counterclockwise. Derive a formula for the constant an- gular acceleration $ \alpha_1 $ [rad/s$^2$] that the driver must have to increase the disc's angular speed from $ \omega_2 $ to $ \omega_3 $ in time t [s]. Express the result in terms of $ r_1 $, $ r_2 $, $ \omega_1 $, $ \omega_3 $, and t.

          2.
17.42 A disc drive is driven by a friction driver, as shown
in Fig. P17.42. Initially, the angular velocity of the disc is
$ \omega_2 $ [rad/s], clockwise, and that of the driver is $ \omega_1 $ [rad/s],
counterclockwise. Derive a formula for the constant an-
gular acceleration $ \alpha_1 $ [rad/s$^2$] that the driver must have to
increase the disc's angular speed from $ \omega_2 $ to $ \omega_3 $ in time t
[s]. Express the result in terms of $ r_1 $, $ r_2 $, $ \omega_1 $, $ \omega_3 $, and t.

2.
17.42 A disc drive is driven by a friction driver, as shown
in Fig. P17.42. Initially, the angular velocity of the disc is
ω2 [rad/s], clockwise, and that of the driver is ω1 [rad/s],
counterclockwise. Derive a formula for the constant an-
gular acceleration α1 [rad/s^2] that the driver must have to
increase the disc's angular speed from ω2 to ω3 in time t
[s]. Express the result in terms of r1, r2, ω1, ω3, and t.

Added by Mercedes G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supratim Pal

07/05/2023

Step 1

The linear velocity of the disc is $v_2 = r_2\omega_2$. Since the disc and the driver are in contact, their linear velocities at the point of contact must be equal. Therefore, $v_1 = v_2$, which implies $r_1\omega_1 = r_2\omega_2$. Show more…

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17.42 A disc drive is driven by a friction driver, as shown in Fig. P17.42. Initially, the angular velocity of the disc is $\omega_2$ [rad/s], clockwise, and that of the driver is $\omega_1$ [rad/s], counterclockwise. Derive a formula for the constant angular acceleration $\alpha_1$ [rad/s²] that the driver must have to increase the disc's angular speed from $\omega_2$ to $\omega_3$ in time t [s]. Express the result in terms of $r_1$, $r_2$, $\omega_1$, $\omega_3$, and t.