Circular & Rotational Motion Review (April 6, 2022)

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

• 7.3 × 10⁻⁵ rad/s

• 3.6 × 10⁻⁵ rad/s

• 6.28 × 10⁻⁵ rad/s

• 3.14 × 10⁻⁵ rad/s

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 5.0-s interval?

• 12.5 rad

• 25 rad

• 2.0 rad

• 0.50 rad

A fan blade, initially at rest, rotates with a constant acceleration of 0.025 rad/s². What is the time interval required for it to reach a 4.2-rad displacement after starting from rest?

• 1.8 s

• 2.0 s

• 16 s

• 18 s

A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.20 m from the center of the same wheel?

• 1.0 m/s

• 1.3 m/s

• 2.7 m/s

• 8.0 m/s

Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point.

• Both are constant.

• Only the angular velocity is constant.

• Only the linear velocity is constant.

• Neither is constant.

A point on the rim of a 0.25-m-radius fan blade has centripetal acceleration of 0.20 m/s². Find the centripetal acceleration of a point 0.05 m from the center of the same wheel.

• 0.01 m/s²

• 0.02 m/s²

• 0.04 m/s²

• 0.08 m/s²

A 0.30-kg rock is swung in a circular path and in a vertical plane on a 0.25-m-length string. At the top of the path, the angular speed is 12.0 rad/s. What is the tension in the string at that point?

• 7.9 N

• 16 N

• 18 N

• 83 N

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

• 0.18

• 0.30

• 0.28

• 0.37

At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s²)

• 28°

• 32°

• 16°

• 10°

Consider a child who is swinging. As she reaches the lowest point in her swing:

• the tension in the rope is equal to her weight.

• the tension in the rope is equal to her mass times her acceleration.

• her acceleration is downward at 9.8 m/s²

• none of the above.