Question

Please help I am in a hurry!! Consider the following four objects: a hoop, a solidsphere, a hollow sphere, a flat disk. Each of the objects hasa mass

Other
ANSWERED
asked 2021-01-08
Please help I am in a hurry!!
Consider the following four objects: a hoop, a solidsphere, a hollow sphere, a flat disk. Each of the objects hasa mass M and a radius R. The axis of rotation passes throughthe center of each object, and is perpedicular to the plane of thehoop and the plane of the flat disk. Which object requiresthe largest torque to give it the same angular acceleration. I need to justify my answers and rank the objects starting with theone that requires the largest torque.

Answers (1)

2021-01-09

ok, Net Torque\( = Inertia \times\)\(\displaystyle\alpha\)
Inertia Hoop= \(\displaystyle{M}{R}^{{{2}}}\)
Inertia Solid Sphere= \(\displaystyle{\left({\frac{{{2}}}{{{5}}}}\right)}\cdot{M}{R}^{{{2}}}\)
Inertia Hollow Sphere= \(\displaystyle{\left({\frac{{{2}}}{{{3}}}}\right)}\cdot{M}{R}^{{{2}}}\)
Inertia Disk= \(\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}\cdot{M}{R}^{{{2}}}\)
If all 4 objects have equal alphas(angular acceleration), then theone with the highest Inertia will have the greatest torque, sincethey all involve \(MR^{2}\), just compare the coefficients...
\(\displaystyle{1}{>}{\left({\frac{{{2}}}{{{3}}}}\right)}{>}{\left({\frac{{{1}}}{{{2}}}}\right)}{>}{\left({\frac{{{2}}}{{{5}}}}\right)}\).....thus the rank would be

\(Hoop>Hollow\ Sphere>Disk>Solid\ Sphere\)
Hey
The one that requires the highest amount of torque is: a hoop, thin/hollow sphere, disc, solid sphere.
The reason for this is that the moment of inertia is the highestfor the hoop, and then goes down as follows moment of inertia is know as I, and the equation is \(I=constant\times M\times R^{2}\), the constant varies for the type of object and itcan be found in most physics books.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-04-21
The crane shown in the drawing is lifting a 182-kg crate upward with an acceleration of \(\displaystyle{1.5}\frac{{m}}{{s}^{{2}}}\). The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound ontoa hollow cylindrical drum that is mounted on the deck of the crane.The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counter clockwise torque to the drum in order towind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.
asked 2021-05-08
A high-speed sander has a disk 4.00 cm in radius that rotates about its axis at aconstant rate of 1265 rev/min.Determine
(a) the angular speed of the disk in radians persecond,
rad/s
(b) the linear speed of a point 2.2 cmfrom the disk's center,
m/s
(c) the centripetal acceleration of a point on the rim, and
\(\displaystyle\frac{{m}}{{s}^{{{2}}}}\)
(d) the total distance traveled by a point on the rim in1.96 s.
m
asked 2021-02-19
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of \(\displaystyle{1950}\ {N}\cdot{m}\) to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?
asked 2021-05-04
Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle. The ball is accelerated uniformly from rest to 10.0 m/s in 0.350 s, at which point it is released. Calculate (a) the angular acceleration of the arm, and (b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.
...