Exam 5: Circular Motion

The Crab Pulsar is a neutron star, rotating with a period of about 33.085 ms. It is estimated to have an equatorial radius of 15 km, about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest 9.5 × 10¹⁰ s in the future. Assuming it is slowing with a constant angular acceleration, what is the tangential acceleration of an object on the neutron star's equator?

At what distance from the center of the Earth would one's weight be half that recorded on the Earth's surface? Let the Earth's radius be R.

An airplane flies in a vertical, semicircular arc in order to simulate "weightlessness" for its occupants. If the radius of the semicircular path it flies is 3500 m, what is the speed at which the plane flies?

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point 4.00 cm from the center, at the time 10.0 seconds from the start?

A 4.00 kg mass is moving in a circular path of radius 2.50 m with a constant angular speed of 5.00 rad/sec. The magnitude of the radial force on the mass is

An object is moving in a circular path with a radius of 4.0 m. If the object moves through an angle of 45 degrees, then the angle in radians is

A car travels at 17 m/s without skidding around a 35 m radius unbanked curve. What is the minimum value of the static friction coefficient between the tires and the road?

An airplane is traveling at 150 m/s in level flight. In order to make a change in direction, the airplane travels in a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal radial acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 12.0 degrees, then the radius of curvature of the curved path of the airplane is

The Crab Pulsar is a neutron star, rotating with a period of about 33.085 ms. It is estimated to have an equatorial radius of 15 km, about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest 9.5 × 10¹⁰ s in the future. What is the magnitude of the average angular acceleration in this situation?

A 0.500 kg stone is moving in a vertical circular path attached to a string that is 75.0 cm long. The stone is moving around the path at a constant frequency of 2.20 rev/sec. At the moment the stone is overhead, the stone is released. The velocity of the stone when it leaves the circular path is

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the magnitude of the (total) acceleration of a point 4.00 cm from the center at the time 30.0 seconds from the start?

A 4.00 kg mass is moving in a circular path with a constant angular speed of 5.00 rad/sec and with a linear speed of 5.00 m/sec. The magnitude of the radial force on the mass is

A 2.60 kg mass is moving in a circular path with a constant angular speed of 5.50 rad/sec and with a linear speed of 3.50 m/s. The magnitude of the radial force on the mass is

A 4.0 kg mass is moving in a circular path of radius 2.5 m with a constant linear speed of 5.0 m/s. The magnitude of the radial force on the mass is

A 2000 kg car is traveling on a curved, icy road without sliding. The speed of the car is 30 m/s and the road is banked at an angle of 20.0 degrees. The radius of curvature of the road is

A conical pendulum is constructed by attaching a mass to a string 2.5 m in length. The mass set in motion in a horizontal circular path about the vertical axis. If the angular speed of the conical pendulum is a constant 2.8 rad/s, then the angle the string makes with the vertical axis is

A car travels around a 35 m radius unbanked curve. The static friction coefficient between the tires and the road is 0.45. What is the maximum speed at which the car can travel without slipping around this curve?

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 4.00 rotations per second, then the linear speed of a point on the circumference is

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the linear speed of a point 4.0 cm from the center at the time 10.0 seconds from the start?

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 15.0 seconds from the start?