Answer:
the correct statement is 2. The solid plate will have the greater angular acceleration.
the correct phrase is 4. The plate with the hole has its mass distributed further out from the axis of rotation, which will increase its moment of inertia.
Explanation:
Newton's second law expression for rotational motion is
τ = I α (1)
where the torque is
τ = F r
in this case, as the discs have the same radius and the applied force is the same, the torque is the same on the two discs.
The moment of inertia is given by the expression
I =∫ r² dm
for bodies with high symmetry are tabulated
the moment of inertia for in disk solid is I₁ = ½ m R₂²
the moment for a disk with a hole I₂ = ½ m (R₁² + R₂²)
We can see that the moment of inertia of the disk with the hole is greater than the moment of inertia of the solid disk.
Let's use equation 1
α = τ/I
therefore the angular acceleration is lower for the body with the higher moment of inertia, consequently the solid disk has higher angular acceleration
the correct statement is 2
The reason is because the moment of inertia is higher for the hollow disk.
the correct phrase is 4
B.sunnny cold probable rain
A joule is a unit of energy.
A car moves along an x axis through a distance of 900 m, starting at rest (at x = 0) and ending at rest (at x = 900 m). Through the first 1/4 of that distance, its acceleration is +6.25 m/s2. Through the next 3/4 of that distance, its acceleration is -2.08 m/s2. What are (a) its travel time through the 900 m and (b) its maximum speed?
<span>Solve for the time at the 1/4 mark. That's 225 m. How? d = (1/2)at^2 ( initial velocity zero). Thus 225 = (1/2) 6.25 t^2. t^2 = ( 225 * 2 ) / 6.25. t = 8.5 sec. </span>
<span>At the other end t^2 = (675 * 2) / 2.08 -- we reversed the sign and ran time backwards. t = 25.5 sec. </span>
<span>So total time is 8.5 + 25.5 or 34 sec. </span>
<span>Since zero initial velocity: v^2 = 2 a d. Here, v^2 = 2 * 6.25 * 225. v = 53 m/s. That's the fastest speed since braking then occurs.</span>