Please answer all the questions 4 . A uniform solid disk rolls without slipping
ID: 1790900 • Letter: P
Question
Please answer all the questions
4. A uniform solid disk rolls without slipping down a 17.0° inclined plane. What is the acceleration of the disk's center of mass?
The moment of inertia of a uniform solid disk about an axis that passes through its center = ½mr².
The moment of inertia of a uniform solid disk about an axis that is tangent to its surface = 32mr².
m/s²
5. Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.60 kg.m² and an angular velocity of +8.00 rad/s. Disk B is rotating with an angular velocity of 10.0 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocity of 2.3 rad/s. The axis of rotation for this unit is the same as that for the separate disks. What is the moment of inertia of disk B?
kg.m2
6. The period of oscillation of a given mass that is connected to a vertical spring (k1 = 280 N/m) is 2.00 s. If the same mass were instead suspended from a different spring (k2 = 450 N/m), what would be the period of oscillation?
s
7. An object of mass 0.46 kg is attached to a horizontal spring, with spring constant 50.0 N/m. If the object is stretched 3.20 cm from the equilibrium position and released, what is its maximum speed?
m/s
Explanation / Answer
4. along the incline, Fnet = m a
m g sin17 - f = m a .... (i)
and net torque = I alpha
r f = (n m r^2) (a/r)
f = (n m ) a
putting in(i),
m g sin17 = m a (n + 1)
a = g sin17 / (n + 1)
when I = 1/ m r^2 => n = 0.5
a = 1.91 m/s^2