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A new car is tested on a 230-m-diameter track. If the car speeds up at a steady $1.56 \, m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration? </a> </h3> <a class="elementor-post__read-more" href="https://nerd-notes.com/ubq/35738/" aria-label="Read more about A new car is tested on a 230-m-diameter track. If the car speeds up at a steady <span class="katex-eq" data-katex-display="false"></span> 1.56 \, m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?" tabindex="-1" target="_blank"> Read More > </a> </div> </div> </article> <article class="elementor-post elementor-grid-item post-35712 ubq type-ubq status-publish format-standard hentry topic-centripetal topic-gravitation"> <div class="elementor-postcard"> <div class="elementor-posttext"> <h3 class="elementor-post__title"> <a href="https://nerd-notes.com/ubq/35712/" target="_blank"> A [katex] 2.2 \times 10^21 \, \text{kg}$ moon orbits a distant planet in a circular orbit of radius $1.5 \times 10^8 \, \text{m}$ . It experiences a $1.1 \times 10^19 \, \text{N}$ gravitational pull from the planet. What is the moon’s orbital period in earth days?

A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed. What is the ratio of the normal force to the gravitational force?

A pendulum consists of a ball of mass m suspended at the end of a massless cord of length L as shown. The pendulum is drawn aside through an angle of 60° with the vertical and released. At the low point of its swing, the speed of the pendulum ball is

On a harsh winter day, a 1500 kg vehicle takes a circular banked exit ramp (radius R = 150 m; banking angle of 10 degrees) at a speed of 30 mph, since the speed limit is 35 mph. However, the exit ramp is completely iced up (= frictionless). To make matters worse, a wind is blowing parallel to the ramp in a downward direction. The wind exerts a force of 3000 N. Under these conditions, can the driver continue to follow a safe horizontal circle on the exit ramp and stay below the speed limit? To convert mph into m/s use 1 mi = 1607 m and 1 hr is 3600 s.

Friction provides the force needed for a car to travel around a flat, circular race track.

A 2 kg ball is swung in a vertical circle. The length of the string the ball is attached to is 0.7 m. It takes 0.4 s for the ball to travel one revolution (we will assume constant speed)

A compressed spring mounted on a disk can project a small ball. When the disk is not rotating, as shown in the top view above, the ball moves radially outward. The disk then rotates in a counterclockwise direction as seen from above, and the ball is projected outward at the instant the disk is in the position shown above. Which of the following best shows the subsequent path of the ball relative to the ground?

An 80 kg person sits in a swing that goes around in a circle. The chain connecting the string to the center (so the length of the string) of the ride is 8 m long and it makes and angle of 40° with the horizontal. What is the speed of the person going around in a circle?

A communications satellite orbits the Earth at an altitude of 35,000km above the Earth’s surface. Mass Earth= $6 \times 10^{24} \text{ kg}$ & Radius Earth= $6.4 \times 10^6 \text{ m}$ . What is the satellite’s velocity?

A planet of constant mass orbits the sun in an elliptical orbit. Neglecting any friction effects, what happens to the planet’s rotational kinetic energy about the sun’s center?

A car moves at constant speed in a circle of radius 75 m on a horizontal road. The coefficient of static friction is 0.62. Find the maximum speed the car can go without sliding.

A car is moving up the side of a circular roller coaster loop of radius 12 m. The angular velocity is 1.8 rad/s and angular acceleration is -0.82 rad/s?. The car is at the same elevation as the center of the loop. Find the magnitude and direction of the acceleration.

A 2.0 kg ball on the end of a 0.65 m long string is moving in a vertical circle. At the bottom of the circle, its speed is 4.0 m/s. Find the tension in the string.

A discus is held at the end of an arm that starts at rest. The average angular acceleration of $54 \, \text{rad/s}^2$ lasts for 0.25 s. Find the average tangential acceleration. Find the speed at release. Find the centripetal acceleration just before release. The path is circular and has radius 1.1 m.

A simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. The pendulum is held at an angle of 30° from the vertical by a light horizontal string attached to a wall, as shown above.

A linear spring of negligible mass requires a force of 18.0 N to cause its length to increase by 1.0 cm. A sphere of mass 75.0 g is then attached to one end of the spring. The distance between the center of the sphere M and the other end P of the un-stretched spring is 25.0 cm. Then the sphere begins rotating at constant speed in a horizontal circle around the center P. The distance P and M increases to 26.5

The diagram above shows a marble rolling down an incline, the bottom part of which has been bent into a loop. The marble is released from point A at a height of 0.80 m above the ground. Point B is the lowest point and point C the highest point of the loop. The diameter of the loop is 0.35 m. The mass of the marble is 0.050 kg. Friction forces and any gain in kinetic energy due to the rotating of the marble can be ignored. When answering the following questions, consider the marble when it is at point C.

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the radius of a geosynchronous orbit about the neutron star?

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the speed of a point on the equator of the star?

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but well approximate it as a 50 km diameter circular orbit with a period of 11 days.

Which of the following do not affect the maximum speed that a car can drive in a circle? Choose both correct answers.

Which of the following best explains why astronauts experience weightlessness while orbiting the earth?

A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible?

A curve with a radius of 125 m is properly banked for a car traveling 40 m/s. What must be the coefficient of static friction for a car not to skid when traveling at 53 m/s?

A ball of mass M is attached to a string of length L. It moves in a vertical circle and at the bottom the ball just clears the ground. The tension at the bottom of the path is 3 times the weight of the ball. Give all answers in terms of M, L, and g.

Riders in a carnival ride stand with their backs against the wall of a circular room of diameter 8.0 m. The room is spinning horizontally about an axis through its center at a rate of 45 rev/min when the floor drops so that it no longer provides any support for the riders. What is the minimum coefficient of static friction between the wall and the rider required so that the rider does not slide down the wall?

A 250 newton centripetal force acts on a car moving at a constant speed in a horizontal circle. If the same force is applied, but the radius is made smaller, what happens to the speed, v, and the frequency, f, of the car?

Suppose you are a passenger traveling in car along a road that bends to the left. Why will you feel like you are being thrown against the door. What causes this force?

A delivery truck is traveling north. It then turns along a leftward circular curve. This the packages in the truck to slide to the RIGHT. Which of the following is true of the net force on the packages as they are sliding?

A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy (in terms of T, R, and g)?

A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a 4 kg chair which hangs freely from a 10 m long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every 3 seconds. When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs 90kg. Has the operator shown that the ride is safe for a 25 kg child?

Refer to the diagram above and solve all equations in-terms of R, M, k, and constants. What is the speed mass 2M as it reaches point B? Calculate the tension in the string supporting mass 2M as it reaches point B. Mass 2M collides with a smaller mass M at point B. After the collision, mass 2M has a speed equal to 1/3 its original value before the collision. What is the speed of mass M after the collision? Mass M then moves along the ground without friction with the speed found in #3 above, until it collides with the spring. Determine the maximum compression of the spring at C.

A ball of mass m is fastened to a string. The ball swings at constant speed in a vertical circle of radius R with the other end of the string held fixed. Neglecting air resistance, what is the difference between the string’s tension at the bottom of the circle and at the top of the circle?

Two satellites are in circular orbits around Earth. Satellite A has speed vA . Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?

A 2.2 kg ball on the end of a 0.35 m long string is moving in a vertical circle. At the bottom of the circle, its speed is 5.3 m/s. Find the tension in the string.

A person’s back is against the inner wall of spinning cylinder with no support under their feet. If the radius is R, find an expression for the minimum angular speed so the person does not slide down the wall. The coefficient of static friction is µs.

The distance from earth to sun is 1.0 AU. The distance from Saturn to sun is 9 AU. Find the period of Saturn’s orbit in years. You can assume that the orbits are circular.

Find the escape speed from a planet of mass 6.89 x 1025 kg and radius 6.2 x 106 m.

A block starts at rest on a frictionless inclined track which then turns into a circular loop of radius R and is vertical. In terms of R and constants, find the minimum height h above the bottom of the loop the block must start from so it makes it around the loop.

A satellite circling Earth completes each orbit in 132 minutes. Find the altitude of the satellite. What is the value of g at the location of this satellite?

A car is safely negotiating an unbanked circular turn at a speed of 17 m/s on dry road. However, a long wet patch in the road appears and decreases the maximum static frictional force to one-fifth of its dry-road value. If the car is to continue safely around the curve, to what speed must the driver slow the car?

An airplane can safely bank when subjected to a centripetal acceleration of 8 g’s. If the airplane flies at a constant speed of 400 m/s, how long does it take to make a 180° turn?

An Olympic bobsled team goes through a horizontal curve at a speed of 120 km/hr. If the radius of curvature is 10.0 m, what is the apparent weight the crew experiences-express in terms of mg.

What is a man’s apparent weight at the equator if his weight is 500 N? The earth’s radius is 6.37 x 106 m.

A rock is whirled on the end of a string in a horizontal circle of radius R with a constant period T. If the radius of the circle is reduced to R/3, while the period remains T, what happens to the centripetal acceleration (ac) of the rock?

Two object rests on a platform rotating at constant speed. Object A is at distance of half the platform’s radius from the center. Object B lays at edge of the platform. Assuming the platform continues rotating at the same speed, how does the centripetal force of the two objects compare?

Two wires are tied to the 500 g sphere shown below. The sphere revolves in a horizontal circle at a constant speed of 7.2 m/s. What is the tension in the upper wire? What is the tension in the lower wire?

The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. Suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 60000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples?

A concrete highway curve of radius 60.0 m is banked at a 12.0 ° angle. What is the maximum speed with which a 1300 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)