Why is it harder to unscrew a tight screw with a screwdriver than to unscrew a t

Question

Why is it harder to unscrew a tight screw with a screwdriver than to unscrew a tight bolt with a wrench? A wooden disk of mass 5.00 kg and radius 30.0 cm is initially spinning clockwise on an axle with angular velocity 6.12 rad/s. Friction from the axle exerts an average torque of 2.38 N m. (a) What is the direction of the torque? (b) What is the total work done by friction once the wheel has stopped? In a binary star system, two stars both orbit around their center of mass. Say two stars each of a mass of about 5.73 times 10^31 kg, are orbiting each other with a distance between them of 1.56 times 10^12 m. What is the period of orbit for the two stars? A pendulum is made massless string of length 0.955 m with a mass 1.53 kg attached to the end. What is the magnitude of the torque from gravity if the pendulum is making an angle of 60.0 degree with the vertical? Two identical masses are attached on either end of a massless rod. Will the tension in the rod be larger if the object is rotated around the center of the rod or the end of the rod? Explain your answer. One common idea to create artificial gravity on a spaceship is to rotate the ship about its center. Let's say a part of a spaceship is a ring with a radius of 205 m. How quickly would the ring have to spin to simulate the gravity on Earth? Suppose we have a race rolling the following objects down a ramp: a solid cylinder with mass 2.0kg and radius 5.2 cm, a thin hollow cylinder with mass 5.3g and radius 0.2 m, a uniform ball of mass 3.5 kg and radius 0.54 m, and a thin ring of mass 1.0 kg and radius 0.8 m. What will be the results of the race? When a yo-yo is thrown, it unwinds its string as it falls. If the yo-yo travels downward with a linear speed of 1.0 m/s, what is the tangential speed of the outer edge of the yo-yo? The yo-yo has an outer radius of 5.0 cm and an inner radius (that the string wraps around) of 1.5 cm. A woman is holding an axle with a bike tire on it, which can freely rotate (without friction). She exerts an average torque on the tire of 2.37 N m, and in 0.302 s, the tire goes from having no angular velocity to having an angular velocity of 6.22 rev/s. If the radius of the tire is 0.675 m, what is its mass? You can approximate the bike tire as a thin ring.

Explanation / Answer

Q1:

It is because in case of a screw driver the force arm (length from the application of force) is less in this case
while as in case of a wrench the force arm is greater which enables more torque hence easy removal.

Q2

The two stars will rotate in a circle due to mutual force of gravitation .
The radius of the circle will half of distance between the two.
Thus
Force is Gmm/r^2.
where m is mass of each star=5.73*10^31 kg and r is the radius of circle=(1.56*10^12)/2=0.78*10^12m.

Now the accelration is given as Gm/r^2= angular velocity square * r
= 4*(pi*freq)^2 *r
T^2 = (4 * pi^2 * r^3)/Gm
=(1.87 * 10^37)/ 3.87*10^21
=4.83*10^15
=69498201.4156 sec
=804.37 days
=2.2 years.

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