BackThe angular acceleration of a wheel, as a function of time, is α = 4.2 t² ― 9.0 t , where α is in rad/s² and t in seconds. If the wheel starts from rest (θ = 0 , ω = 0, at t = 0), determine a formula for the angular position θ, both as a function of time.
Suppose the force Fₜ in the cord hanging from the pulley of Example 10–10, Fig. 10–22, is given by the relation Fₜ = 3.00 t ― 0.20 t² (newtons) where t is in seconds. If the pulley starts from rest, what is the linear speed of a point on its rim 9.0 s later? Ignore friction and use the moment of inertia, calculated in Example 10–10.
The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–52. The wheel has angular velocity ω₁ = 48.0 rad/s about its axle, and the turntable has angular velocity ω₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) What are the directions of and at the instant shown?
The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–52. The wheel has angular velocity ω₁ = 48.0 rad/s about its axle, and the turntable has angular velocity ω₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure? What is the resultant angular velocity of the wheel, as seen by an outside observer, at the instant shown? Give the magnitude and direction.
The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–52. The wheel has angular velocity ω₁ = 48.0 rad/s about its axle, and the turntable has angular velocity ω₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) What is the magnitude and direction of the angular acceleration of the wheel at the instant shown? Take the 𝒵 axis vertically upward and the direction of the axle at the moment shown to be the 𝓍 axis pointing to the right.