PHYS 3

The flywheel of an engine has a moment of inertia 2.70 kg⋅m^2 about its rotation axis.
A) What constant torque is required to bring it up to an angular speed of 400 rev/min in a time of 7.50 s , starting from rest?
B) What is its final kinetic energy?

A uniform disk with mass 43.9 kg and radius 0.210 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 32.5 N is applied tangent to the rim of the disk.
A) What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.400 revolution?
B)What is the magnitude a of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.400 revolution?

A wheel with a weight of 392 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular velocity of 28.0 rad/s . The radius of the wheel is 0.604 m and its moment of inertia about its rotation axis is 0.800 MR2. Friction does work on the wheel as it rolls up the hill to a stop, at a height of h above the bottom of the hill; this work has a magnitude of 3490 J .
A) Calculate h.
Use 9.81 m/s^2 for the acceleration due to gravity.

The engine of an aircraft propeller delivers an amount of power 180 hp to the propeller at a rotational velocity of 2380 rev/min .
A) How much torque does the aircraft engine provide?
B) How much work does the engine do in one revolution of the propeller?

A) Compute the torque developed by an industrial motor whose output is 175 kW at an angular speed of 5000 rev/min .
B) A drum with negligible mass, 0.480 m in diameter, is attached to the motor shaft, and the power output of the motor is used to raise a weight hanging from a rope wrapped around the drum. How heavy a weight can the motor lift at constant speed?
C) At what constant speed will the weight rise?

A majorette in a parade is performing some acrobatic twirlings of her baton. Assume that the baton is a uniform rod of mass 0.120 kg and length 80.0 cm .
A) Initially, the baton is spinning about a line through its center at angular velocity 3.00 rad/s . What is its angular momentum?
B) With a skillful move, the majorette changes the rotation of her baton so that now it is spinning about an axis passing through its end at the same angular velocity 3.00 rad/s as before. What is the new angular momentum of the rod?

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 10^14 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 8.0×10^5 km (comparable to our sun); its final radius is 15 km .
A) If the original star rotated once in 28 days, find the angular speed of the neutron star.

A small 13.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 70.0 g and is 120 cm in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 25.0 cm/s relative to the table.
A) What is the angular speed of the bar just after the frisky insect leaps?

An airplane propeller is 2.20 m in length (from tip to tip) with mass 112 kg and is rotating at 2500 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod.
A) What is its rotational kinetic energy?
B) Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

In Parts A, B, C consider the following situation. In a baseball game the batter swings and gets a good solid hit. His swing applies a force of 12,000 N to the ball for a time of 0.70×10^−3s.
A) Assuming that this force is constant, what is the magnitude J of the impulse on the ball?
B) Now assume that the pitcher in Part D throws a 0.145-kg baseball parallel to the ground with a speed of 32 m/s in the +x direction. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. What is the ball's velocity just after leaving the bat if the bat applies an impulse of −8.4N⋅s to the baseball?

Find the required angular speed, ω, of an ultracentrifuge for the radial acceleration of a point 3.00 cm from the axis to equal 5.00×10^5 g (where g is the acceleration due to gravity).

A) What is the magnitude of the momentum of a truck of mass 1.15×10^4 kg whose speed is 10.0 m/s ?
B) What speed would a sport utilitiy vehicle of mass 2500 kg have to attain in order to have the same momentum?
C) What speed would a sport utility vehicle of mass 2500 kg have to attain in order to have the same kinetic energy?

A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is −6.00rad/s at t=0, increases linearly with time and is +8.00rad/s at t=7.00s. We have taken counterclockwise rotation to be positive.
A) Find the duration of the time interval when the speed of the wheel is increasing?
B) Find the duration of the time interval when the speed of the wheel is decreasing?
C) What is the angular displacement of the wheel at t=7.00s?

A baseball has mass 0.143 kg .
A) If the velocity of a pitched ball has a magnitude of 45.5 m/s and the batted ball's velocity is 54.0 m/s in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat.
B) If the ball remains in contact with the bat for 2.1 ms , find the magnitude of the average force applied by the bat.

On a frictionless horizontal air table, puck A (with mass 0.249 kg ) is moving toward puck B (with mass 0.373 kg ), which is initially at rest. After the collision, puck A has velocity 0.121 m/s to the left, and puck B has velocity 0.655 m/s to the right.
A )What was the speed vAi of puck A before the collision?
B) Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

A spring-loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in the air, as shown in (Figure 1) . The spring has spring constant k=667N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0 and then released, the ball reaches a maximum height hmax.
A) Find v_m the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y=0).
B) Find the maximum height hmax of the ball.

A physics professor stands at the center of a frictionless turntable
with arms outstretched and a 5.0-kg dumbbell in each hand
(Fig. 10.29). He is set rotating about the vertical axis, making one
revolution in 2.0 s. Find his final angular velocity if he pulls the
dumbbells in to his stomach. His moment of inertia (without the
dumbbells) is 30 kg*m^2 with arms outstretched and 2.2 kg*m^2
with his hands at his stomach. The dumbbells are 1.0 m from the
axis initially and 0.20 m at the end.

A door 1.00 m wide, of mass 15 kg, can rotate freely about a vertical
axis through its hinges. A bullet with a mass of 10 g and a
speed of 400 m/s strikes the center of the door, in a direction perpendicular
to the plane of the door, and embeds itself there. Find
the door’s angular speed. Is kinetic energy conserved?

The rotating blade of a blender turns with constant angular
acceleration 1.50 rad/s^2 (a) How much time does it take to reach
an angular velocity of 36.0 rad/s, starting from rest? (b) Through
how many revolutions does the blade turn in this time interval?

A classic 1957 Chevrolet Corvette of mass 1240 kg starts
from rest and speeds up with a constant tangential acceleration of 2 m/s^2
on a circular test track of radius 60.0 m. Treat the car as
a particle. (a) What is its angular acceleration? (b) What is its
angular speed 6.00 s after it starts? (c) What is its radial acceleration
at this time? (d) Sketch a view from above showing the circular
track, the car, the velocity vector, and the acceleration component
vectors 6.00 s after the car starts. (e) What are the magnitudes of
the total acceleration and net force for the car at this time? (f) What

A 1500-kg sedan goes through a
wide intersection traveling from north to south when it is hit by a
2200-kg SUV traveling from east to west. The two cars become
enmeshed due to the impact and slide as one thereafter. On-thescene
measurements show that the coefficient of kinetic friction
between the tires of these cars and the pavement is 0.75, and the
cars slide to a halt at a point 5.39 m west and 6.43 m south of
the impact point. How fast was each car traveling just before the
collision?