Answer True, False, or Cannot tell to each of the four statements below. Q1) A w

Question

Answer True, False, or Cannot tell to each of the four statements below. 

Q1) A wheel turns on a frictionless axle. A string wrapped around the rim of the wheel is connected to a mass. The mass is released at t=0 and hits the floor at t=t1. The graph shows a possible - t behaviour for this situation.

Q2) The solid cylinders and the cylindrical shells have the same mass, the same radius, and turn on frictionless axles. A rope is wrapped around each of them and is acted on as shown.
Cylinder shell 3 has the smallest angular acceleration.

Q3) If force F1 was reversed, the object would not rotate about the axle.
(Note:F1  =  F2 < F3)

Q4) A square plate can rotate about an axle through its centre. One of three forces of equal magnitude can be applied to the plate, as shown.
If F1 is applied at the same spot, but normal to the edge, the plate will not rotate.

Please do not just give me the answer. Explain what is happening, and provide formulas and principles if applicable.

Thank you.

Explanation / Answer

1) balancing torque on wheel,

torque = I x alpha

r x T = I x alpha

T = I*alpha / r

on hanging mass,

mg - T = ma

mg - ( I*alpha / r) = ( m * alpha * r)

mg = alpha( I/r + mr )

alpha = mg / ( I /r + mr)

here everything m, g , I and r are constant.

so angular acceleration ( alpha) will be constant.

alpha = mg / ( I /r + mr) = k
using wf = wi + alpha*t

w = 0 + kt

so this will be straight line with slope k from 0 to t1.

SO this diagram is correct.

2) moment of inertia for solid Is = m r^2 /2

for hollow cylinder, Ih = m r^2

for1:
on cylinder using torque = I x alpha

r x T = ( m r^2 /2) ( alpha1)

T = m*alpha1*r / 2

for mass: mg - T = ma

10 - m*alpha1*r / 2 = 10*alpha1*r /10

alpha1 = 2*10 / 3r   = 20 / ( 2r + mr)

for2:

T = 10 N

r x 10 = mr^2 /2 * alpha2

alpha2 = 20 / mr

for 3:
r x T = ( m r^2) ( alpha1)

T = m*alpha1*r

for mass: mg - T = ma

10 - m*alpha1*r = 10*alpha1*r /10

alpha1 = 10 / ( r + mr)

for 4:

T = 10N

r x10 = mr^2 alpha

alpha = 10 / mr

so cylinder shell 3 has the samllest angular acc.

please don't post many questions in single link.

it will be difficult to answer with full explanation.

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