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A tractor has rear wheels with a radius of 1.00 m and front wheels with a radius of 0.250 m. The rear wheels are rotating at 100 rev min-1. Find (a) the angular speed of the front wheels in revolutions per minute and (b) the distance covered by the tractor in 10.0 min.

Important Questions on Rotation

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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 2
Just as a helicopter is landing, its blades are turning at 30.0 rev s-1 and slowing at a constant rate. In the 2.00 min required for them to stop, how many revolutions do they make?
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 3
When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm, for rotation less than 1 rev, what are the (a) smallest and (b) the largest angular speeds that cause the toast to hit and then topple to be butter-side down?
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 4
The angular position of a point on a rotating wheel is given by θ=2.0+4.0 t2+2.0 t3, where θ is in radians and t is in seconds. At t=0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t=3.0 s. (d) Calculate its angular acceleration at t=4.0 s. (e) Is its angular acceleration constant?
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 5
At time t=0, a rotating bicycle wheel is thrown horizontally from a rooftop with a speed of 49 m s-1. By the time its vertical speed is also 49 m s-1, it has completed 40 revolutions. What has been its average angular speed to that point in the fall?
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 6
A horizontal pottery wheel (a horizontal disk) with a radius of 30.0 cm can rotate about a vertical axis with negligible friction but is initially stationary. A horizontal rubber wheel of radius 2.00 cm is placed against its rim. That wheel is mounted on a motor. When the motor is switched on at time t=0, the rubber wheel undergoes a constant angular acceleration of 5.00 rad s-2. Its contact with the pottery wheel causes the pottery wheel to undergo an angular acceleration. When the pottery wheel reaches an angular speed of 5.00 rev s-1 the rubber wheel is pulled away from contact and thereafter the pottery wheel rotates at 5.00 rev s-1. From t=0 to t=2.00 min, how many full rotations does the pottery wheel make?
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 7

The wheel in the figure shown below has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev s-1. You want to shoot a 20 cm long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin.
(a) What minimum speed must the arrow have? (b) Does it matter where between the axle and rim of the wheel you aim? If so, what is the best location?

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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 8
The angular acceleration of a wheel is α=6.0t4-4.0t2, with α in radians per second-squared and t in seconds. At time t=0, the wheel has an angular velocity of +2.5 rad s-1 and an angular position of +1.5 rad. Write expressions for (a) the angular velocity (rad s-1) and (b) the angular position (in radians) as functions of time.
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Principles Of Physics International Student Version>Chapter 10 - Rotation>Problems>Q 9
In 5.00 s, a 2.00 kg stone moves in a horizontal circle of radius 2.00 m from rest to an angular speed of 4.00 rev s-1. What are the stone's (a) average angular acceleration and (b) rotational inertia around the circle's center?