Rock's Angular Motion in Bicycle Wheel Braking

[freak_boy186]

Homework Statement

A rock stuck in the tread of a 53.0 cm diameter bicycle wheel has a tangential speed of 3.50 m/s. When the brakes are applied, the rock's tangential deceleration is 1.20 m/s^2.

X.) What is the magnitudes of the rock's angular velocity (omega) when t = 1.60s?
Y.) What is the magnitudes of the rock's angular acceleration (alpha) when t = 1.60s?
Z.) At what time is the magnitude of the rock's acceleration equal to g? (9.8 m/s^2)

Homework Equations

v = r(omega)
a = r(omega)^2
Vf = Vi + a[tangental](dt)
D[omega] = alpha(dt)
omega^2 = omega0^2 + 2(alpha)(dtheta)

The Attempt at a Solution

X.) r = 0.265m, a[tangental] = -1.2, Vi = 3.5, dt = 1.6
Vf = 3.5 + (-1.2)(1.6) = 1.58
omega = 1.58/0.265 = 5.962 {incorrect apparently}

Y.) omega1 = 3.5/.265 = 13.208
(13.208 - 5.962) = alpha(1.6)
alpha = 4.528 {incorrect, but expected because X is incorrect}

 

[vela]

Homework Statement

A rock stuck in the tread of a 53.0 cm diameter bicycle wheel has a tangential speed of 3.50 m/s. When the brakes are applied, the rock's tangential deceleration is 1.20 m/s^2.

X.) What is the magnitudes of the rock's angular velocity (omega) when t = 1.60s?
Y.) What is the magnitudes of the rock's angular acceleration (alpha) when t = 1.60s?
Z.) At what time is the magnitude of the rock's acceleration equal to g? (9.8 m/s^2)

Homework Equations

v = r(omega)
a = r(omega)^2
Vf = Vi + a[tangental](dt)
D[omega] = alpha(dt)
omega^2 = omega0^2 + 2(alpha)(dtheta)

The Attempt at a Solution

X.) r = 0.265m, a[tangental] = -1.2, Vi = 3.5, dt = 1.6
Vf = 3.5 + (-1.2)(1.6) = 1.58
omega = 1.58/0.265 = 5.962 {incorrect apparently}

That's correct. Maybe you're not entering it in the right units or with the correct number of significant figures.

Y.) omega1 = 3.5/.265 = 13.208
(13.208 - 5.962) = alpha(1.6)
alpha = 4.528 {incorrect, but expected because X is incorrect}

That's correct too, although you took a roundabout way of calculating it.

 

[freak_boy186]

its asking for omega in rad/sec & alpha in rad/sec^2... would that affect my answers any?

 

[vela]

Nope. Radians is the natural unit for measuring angles.